What is Matrix Multiplication?

Matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix has the number of rows of the first and the number of columns of the second.

For example, a 2x3 matrix can be multiplied by a 3x2 matrix, resulting in a 2x2 matrix.

How to Use the Solver

• Select the dimensions for Matrix A and Matrix B from the dropdown menus.
• Enter the numbers into the input fields for both matrices.
• Click the "Calculate" button.
• The result will appear in the third matrix box.

Rules

• Compatibility: If Matrix A is m×n, Matrix B must be n×p.
• Order Matters: Matrix multiplication is generally not commutative (A×B ≠ B×A).
• Identity Matrix: Multiplying by an identity matrix leaves the original matrix unchanged.