A matrix, which when multiplied by another matrix, results in the identity matrix.
\begin{equation} \mathbf{A}\mathbf{A}^{-1} = I \end{equation}
e.g.
\begin{equation} \begin{bmatrix} a & b\\\ c & d \end{bmatrix} \begin{bmatrix} d & -b\\\ -c & a \end{bmatrix}= \begin{bmatrix} 1 & 0\\\ 0 & 1 \end{bmatrix} \end{equation}