8.
a) The \(2 \times 2\) matrix \(\mathbf { A }\) is given by $$\mathbf { A } = \left( \begin{array} { l l } 7 & 3
2 & 1 \end{array} \right) .$$ The \(2 \times 2\) matrix \(\mathbf { B }\) satisfies $$\mathbf { B } \mathbf { A } ^ { 2 } = \mathbf { A } .$$ Find the matrix \(\mathbf { B }\).
b) The \(2 \times 2\) matrix \(\mathbf { C }\) is given by $$\mathbf { C } = \left( \begin{array} { l l } - 2 & 4
- 1 & 2 \end{array} \right) .$$ By considering \(\mathbf { C } ^ { 2 }\), show that the matrices \(\mathbf { I } - \mathbf { C }\) and \(\mathbf { I } + \mathbf { C }\) are inverse to each other.