Matrix Calculator

Matrices are grids of numbers used for linear algebra. Follow these steps:

Step 1: Define the dimensions of your matrices (Rows and Columns).

Step 2: Enter the values into the grids for Matrix A and Matrix B.

Step 3: Choose the operation: - Addition / Subtraction (requires identical dimensions). - Multiplication (columns of A must match rows of B). - Determinant (square matrices only). - Inverse (square matrices only).

Step 4: Click "Calculate."

Step 5: Review the step-by-step arithmetic showing how each individual cell was calculated.

Matrix operations follow strict rules of alignment:

1. Addition: Add the numbers in the same position: (a_ij + b_ij). 2. Multiplication: The entry in row 'i' and column 'j' of the result is the dot product of row 'i' of Matrix A and column 'j' of Matrix B. 3. Determinant (2x2): ad - bc. 4. Inverse (2x2): (1 / Determinant) * [d, -b; -c, a].

Properties: - Matrix multiplication is NOT commutative (A × B is not the same as B × A). - A matrix must have a non-zero determinant to have an inverse.

The Matrix Calculator is a heavy-duty tool for computer science, engineering, and data analysis. In computer graphics, every movement and rotation of a 3D character is calculated using matrix multiplication. In economics, matrices model the flow of goods across an entire country. This tool eliminates the high risk of human error when performing the dozens of multiplications required for even small 3x3 matrices. By providing the final result and the clear 'dot product' steps, it serves as both a production tool and a learning aid for linear algebra students.