Matrix algebra

Matrix algebra and inverses

Matrices multiply row-by-column. The determinant measures how a matrix scales area (or volume); when it is zero the matrix has no inverse. For $2\times2$, $\mathbf A^{-1}=\frac1{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}$, and inverses solve systems of equations in one step.