3.
$$\mathbf { A } = \left( \begin{array} { l l }
6 & 4
1 & 1
\end{array} \right)$$
- Show that \(\mathbf { A }\) is non-singular.
The triangle \(R\) is transformed to the triangle \(S\) by the matrix \(\mathbf { A }\).
Given that the area of triangle \(R\) is 10 square units, - find the area of triangle \(S\).
Given that
$$\mathbf { B } = \mathbf { A } ^ { 4 }$$
and that the triangle \(R\) is transformed to the triangle \(T\) by the matrix \(\mathbf { B }\),
- find, without evaluating \(\mathbf { B }\), the area of triangle \(T\).