Linear Algebra
Intermediate

2×2 Matrix Product

Product of two 2×2 matrices.

Formula

[abcd][efgh]=[ae+bgaf+bhce+dgcf+dh]\begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}e&f\\g&h\end{bmatrix} = \begin{bmatrix}ae+bg&af+bh\\ce+dg&cf+dh\end{bmatrix}

Variables

a..hEntries

Example

Row times column

Did You Know?

Matrix multiplication is not commutative — swapping the order usually gives a different result, unlike ordinary numbers.

matrix