diff --git a/AGENTS.md b/AGENTS.md
new file mode 100644
index 0000000..5eee74e
--- /dev/null
+++ b/AGENTS.md
@@ -0,0 +1,57 @@
+# AGENTS.md
+
+This file provides instructions for AI agents working with this codebase.
+
+## Project Overview
+
+This is a Vue.js 3 application that functions as a matrix calculator. The core logic is handled by the `mathjs` library. The application is a single-page application (SPA) and does not have a backend.
+
+## Tech Stack
+
+-   **Vue.js 3:** The frontend framework.
+-   **Composition API:** Used for component logic.
+-   **Tailwind CSS:** For styling.
+-   **`mathjs`:** For matrix calculations.
+
+## Folder Structure
+
+-   `src/`: Contains the application source code.
+-   `src/assets/`: Static assets like CSS and images.
+-   `src/components/`: Vue components.
+-   `src/composables/`: Reusable logic, such as matrix operations.
+-   `public/`: Public assets.
+
+## Development
+
+1.  **Install Dependencies:**
+    ```bash
+    npm install
+    ```
+
+2.  **Run the Development Server:**
+    ```bash
+    npm run serve
+    ```
+
+## Linting
+
+To check for code quality and style issues, run the linter:
+
+```bash
+npm run lint
+```
+
+## Key Files
+
+-   `src/App.vue`: The main application component.
+-   `src/components/MatrixInput.vue`: The primary UI component for matrix input and displaying results.
+-   `src/components/OperationButtons.vue`: The component that contains the buttons for performing matrix operations.
+-   `src/composables/useMatrixOperations.js`: The core logic for all matrix calculations resides in this file.
+
+## Coding Conventions
+
+-   Follow standard Vue.js and JavaScript best practices.
+-   Use the Composition API for all new components.
+-   Separate business logic from UI components by using composables.
+-   Ensure that all new features have proper error handling.
+-   Keep the UI clean and user-friendly.
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   App running at:
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-[eslint]
-/app/src/components/MatrixInput.vue
-  174:11  error  'savedMatrix' is assigned a value but never used  no-unused-vars
-
-✖ 1 problem (1 error, 0 warnings)
-
-
-You may use special comments to disable some warnings.
-Use // eslint-disable-next-line to ignore the next line.
-Use /* eslint-disable */ to ignore all warnings in a file.
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-ERROR in [eslint]
-/app/src/components/MatrixInput.vue
-  174:11  error  'savedMatrix' is assigned a value but never used  no-unused-vars
-
-✖ 1 problem (1 error, 0 warnings)
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   App running at:
   - Local:   http://localhost:8080/
   - Network: http://192.168.0.2:8080/
 
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\ No newline at end of file
diff --git a/src/components/MatrixInput.vue b/src/components/MatrixInput.vue
index 2173ca9..763c41d 100644
--- a/src/components/MatrixInput.vue
+++ b/src/components/MatrixInput.vue
@@ -92,6 +92,26 @@
                   </table>
                 </div>
               </div>
+
+              <!-- Vector B -->
+              <div class="flex-1">
+                <h3 class="text-lg font-semibold text-gray-800 mb-3 flex items-center justify-center gap-2">
+                  <i class="fas fa-vector-square"></i> Vector b
+                </h3>
+                <div class="inline-block border-2 border-purple-500 rounded-lg p-3 bg-.050">
+                  <table class="mx-auto">
+                    <tr v-for="(val, i) in vectorB" :key="i">
+                      <td class="p-1">
+                        <input
+                          v-model.number="vectorB[i]"
+                          type="number"
+                          class="w-14 h-10 text-center text-gray-800 border border-gray-300 rounded focus:outline-none focus:ring-2 focus:ring-purple-500 focus:border-purple-500 transition"
+                        >
+                      </td>
+                    </tr>
+                  </table>
+                </div>
+              </div>
             </div>
           </div>
         </div>
@@ -106,8 +126,20 @@
           @solution="handleSolution"
           @eigenvalues="handleEigenvalues"
           @decomposition="handleDecomposition"
+          @error="handleError"
         />
 
+        <!-- Error Display -->
+        <div v-if="error" class="bg-red-100 border-l-4 border-red-500 text-red-700 p-4 rounded-lg shadow-md" role="alert">
+          <div class="flex">
+            <div class="py-1"><i class="fas fa-exclamation-triangle mr-3"></i></div>
+            <div>
+              <p class="font-bold">An error occurred:</p>
+              <p class="text-sm">{{ error }}</p>
+            </div>
+          </div>
+        </div>
+
         <!-- Results Section -->
         <div v-if="operationResult.length || determinant !== null || solution || eigenvalues || lu || qr" class="bg-white rounded-xl shadow-lg overflow-hidden mt-6">
           <div class="bg-gray-800 text-white px-6 py-4 flex items-center">
@@ -166,7 +198,7 @@
 </template>
 
 <script>
-import { createApp, ref, watch } from 'vue';
+import { ref, watch } from 'vue';
 import * as math from 'mathjs';
 import OperationButtons from './OperationButtons.vue';
 
@@ -185,9 +217,15 @@ export default {
     const eigenvalues = ref(null);
     const lu = ref(null);
     const qr = ref(null);
-    const savedMatrix = ref(null);
     const error = ref(null);
 
+    // Load matrix from localStorage on component mount
+    const saved = localStorage.getItem('savedMatrixA');
+    if (saved) {
+      matrixA.value = JSON.parse(saved);
+      matrixSize.value = matrixA.value.length;
+    }
+
     function createMatrix(size) {
       return Array.from({ length: size }, () => Array(size).fill(0));
     }
@@ -245,13 +283,18 @@ export default {
           qr.value = data;
         }
       },
+      handleError(errorMessage) {
+        resetResults();
+        error.value = errorMessage;
+      },
       saveMatrix() {
-        savedMatrix.value = JSON.stringify(matrixA.value);
+        localStorage.setItem('savedMatrixA', JSON.stringify(matrixA.value));
         alert('Matrix A saved successfully!');
       },
       loadMatrix() {
-        if (savedMatrix.value) {
-          matrixA.value = JSON.parse(savedMatrix.value);
+        const saved = localStorage.getItem('savedMatrixA');
+        if (saved) {
+          matrixA.value = JSON.parse(saved);
           matrixSize.value = matrixA.value.length;
           alert('Matrix A loaded successfully!');
         } else {
@@ -270,16 +313,8 @@ export default {
   }
 };
 
-const app = createApp({
-  template: '#app-template',
-  setup() {
-    return {};
-  }
-});
-
-app.mount('#app');
 </script>
 
 <style>
 /* @import url('https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css'); */
-</style>
\ No newline at end of file
+</style>
diff --git a/src/components/OperationButtons.vue b/src/components/OperationButtons.vue
index 8cb7770..2db7cdc 100644
--- a/src/components/OperationButtons.vue
+++ b/src/components/OperationButtons.vue
@@ -27,6 +27,9 @@
         <button @click="calculateEigenvalues">
           <i class="fas fa-chart-line"></i> Eigenvalues (A)
         </button>
+        <button @click="invertMatrix">
+          <i class="fas fa-retweet"></i> Invert (A)
+        </button>
       </div>
     </div>
 
@@ -59,7 +62,8 @@ const emit = defineEmits([
   'operation-result',
   'solution',
   'eigenvalues',
-  'decomposition'
+  'decomposition',
+  'error'
 ])
 
 const { 
@@ -70,7 +74,8 @@ const {
   solveLinearEquations,
   calculateEigenvalues,
   luDecomposition,
-  qrDecomposition
+  qrDecomposition,
+  invertMatrix
 } = useMatrixOperations(props, emit)
 </script>
 
diff --git a/src/composables/useMatrixOperations.js b/src/composables/useMatrixOperations.js
index f2852a2..03fbeb9 100644
--- a/src/composables/useMatrixOperations.js
+++ b/src/composables/useMatrixOperations.js
@@ -6,7 +6,7 @@ export function useMatrixOperations(props, emit) {
       const det = math.det(props.matrixA)
       emit('determinant', det)
     } catch (error) {
-      console.error('Error calculating determinant:', error)
+      emit('error', error.message)
     }
   }
 
@@ -15,7 +15,7 @@ export function useMatrixOperations(props, emit) {
       const result = math.add(props.matrixA, props.matrixB)
       emit('operation-result', result)
     } catch (error) {
-      console.error('Error adding matrices:', error)
+      emit('error', error.message)
     }
   }
 
@@ -24,7 +24,7 @@ export function useMatrixOperations(props, emit) {
       const result = math.subtract(props.matrixA, props.matrixB)
       emit('operation-result', result)
     } catch (error) {
-      console.error('Error subtracting matrices:', error)
+      emit('error', error.message)
     }
   }
 
@@ -33,7 +33,7 @@ export function useMatrixOperations(props, emit) {
       const result = math.multiply(props.matrixA, props.matrixB)
       emit('operation-result', result)
     } catch (error) {
-      console.error('Error multiplying matrices:', error)
+      emit('error', error.message)
     }
   }
 
@@ -43,7 +43,7 @@ export function useMatrixOperations(props, emit) {
       const solution = math.lusolve(props.matrixA, b).toArray().flat()
       emit('solution', solution)
     } catch (error) {
-      console.error('Error solving equations:', error)
+      emit('error', error.message)
     }
   }
 
@@ -56,7 +56,7 @@ export function useMatrixOperations(props, emit) {
       ).join(', ')
       emit('eigenvalues', eigenvalues)
     } catch (error) {
-      console.error('Error calculating eigenvalues:', error)
+      emit('error', error.message)
     }
   }
 
@@ -70,7 +70,7 @@ export function useMatrixOperations(props, emit) {
       }
       emit('decomposition', { type: 'lu', data: lu })
     } catch (error) {
-      console.error('Error performing LU decomposition:', error)
+      emit('error', error.message)
     }
   }
 
@@ -83,7 +83,16 @@ export function useMatrixOperations(props, emit) {
       }
       emit('decomposition', { type: 'qr', data: qr })
     } catch (error) {
-      console.error('Error performing QR decomposition:', error)
+      emit('error', error.message)
+    }
+  }
+
+  async function invertMatrix() {
+    try {
+      const result = math.inv(props.matrixA)
+      emit('operation-result', result)
+    } catch (error) {
+      emit('error', error.message)
     }
   }
 
@@ -95,6 +104,7 @@ export function useMatrixOperations(props, emit) {
     solveLinearEquations,
     calculateEigenvalues,
     luDecomposition,
-    qrDecomposition
+    qrDecomposition,
+    invertMatrix
   }
 }
\ No newline at end of file