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🔢 Matrix Multiplication Calculator

Multiply two 2×2 matrices together and see every element of the resulting product matrix.

Matrix A – Row 1, Col 1

Matrix A – Row 1, Col 2

Matrix A – Row 2, Col 1

Matrix A – Row 2, Col 2

Matrix B – Row 1, Col 1

Matrix B – Row 1, Col 2

Matrix B – Row 2, Col 1

Matrix B – Row 2, Col 2

How 2×2 matrix multiplication works

To multiply two matrices, each element of the resulting matrix is the sum of products between a row from the first matrix and a column from the second. Matrix multiplication is not commutative, meaning A × B usually does not equal B × A.

The formula used

For two 2×2 matrices A and B, each result element is computed as: C[i,j] = (A row i) · (B column j). For example, C[1,1] = a11·b11 + a12·b21, and C[1,2] = a11·b12 + a12·b22, and so on for each position.

This tool is intended for general math and engineering learning purposes. Always double-check critical calculations independently.

Last reviewed August 2026