The transformation T is defined by the matrix \(\mathbf { A }\), where
$$\mathbf { A } = \left[ \begin{array} { r r }
0 & - 1
- 1 & 0
\end{array} \right]$$
Describe the transformation T geometrically.
Calculate the matrix product \(\mathbf { A } ^ { 2 }\).
Explain briefly why the transformation T followed by T is the identity transformation.
The matrix \(\mathbf { B }\) is defined by
$$\mathbf { B } = \left[ \begin{array} { l l }
1 & 1
0 & 1
\end{array} \right]$$
Calculate \(\mathbf { B } ^ { 2 } - \mathbf { A } ^ { 2 }\).
Calculate \(( \mathbf { B } + \mathbf { A } ) ( \mathbf { B } - \mathbf { A } )\).