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 \(G \times G^{-1} = G^{-1} \times G = I_2\).