6.3 Inverses

The inverse of a square matrix $B$ , if it exists and usually written $B^{-1}$ , is that matrix such that $B^{-1} B = I \quad\text{and}\quad B B^{-1} = I.$

Example 6.7 (Matrix inverses) Consider the square matrix $G$ : $G = \left[ \begin{array}{rrr} 4 & 7\\ -2 & 1 \end{array} \right].$ Then the inverse of matrix $G$ is: $G^{-1} = \frac{1}{18} \left[ \begin{array}{rrr} 1 & -7\\ 2 & 4 \end{array} \right],$ since $G \times G^{-1} = G^{-1} \times G = I_2$ .