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