6. Write down the \(2 \times 2\) matrix that represents
- an enlargement with centre \(( 0,0 )\) and scale factor 8 ,
- a reflection in the \(x\)-axis.
Hence, or otherwise,
- find the matrix \(\mathbf { T }\) that represents an enlargement with centre ( 0,0 ) and scale factor 8, followed by a reflection in the \(x\)-axis.
$$\mathbf { A } = \left( \begin{array} { l l }
6 & 1
4 & 2
\end{array} \right) \text { and } \mathbf { B } = \left( \begin{array} { r r }
k & 1
c & - 6
\end{array} \right) , \text { where } k \text { and } c \text { are constants. }$$ - Find \(\mathbf { A B }\).
Given that \(\mathbf { A B }\) represents the same transformation as \(\mathbf { T }\),
- find the value of \(k\) and the value of \(c\).