1. The problem asks us to find the matrix $C$ which results from applying matrix $A$ (anticlockwise rotation by 90°) followed by matrix $B$ (reflection in the line $y = -x$), i.e., $C = B \times A$. 2. Matrices given are: $$ A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix} $$ 3. Compute the product $C = B A$: $$ C = \begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix} \times \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} = \begin{bmatrix} (0 \times 0) + (-1 \times 1) & (0 \times -1) + (-1 \times 0) \\ (-1 \times 0) + (0 \times 1) & (-1 \times -1) + (0 \times 0) \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} $$ 4. Geometrically, the matrix $C = \begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$ represents a reflection about the $y$-axis. This is because multiplication of a vector $\begin{bmatrix} x \\ y \end{bmatrix}$ by $C$ yields $\begin{bmatrix} -x \\ y \end{bmatrix}$ which is a mirror image about the $y$-axis. \n**Final answers:** (i) $$ C = \begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} $$ (ii) The single transformation represented by $C$ is a reflection about the $y$-axis.