(a) Write down the matrix A of the linear transformation \(A(x, y) \to (2x -y, -5x + 3y)\). (b) If \(B = \begin{pmatrix} 3 & 1 \\ 5 & 2 \end{pmatrix}\), fin...

(a) Write down the matrix A of the linear transformation \(A(x, y) \to (2x -y, -5x + 3y)\).

(b) If \(B = \begin{pmatrix} 3 & 1 \\ 5 & 2 \end{pmatrix}\), find :

(i) \(A^{2} - B^{2}\) ; (ii) matrix \(C = B^{2} A\) ; (iii) the point \(M(x, y)\) whose image under the linear transformation \(C\) is \(M' (10, 18)\).

(c) What is the relationship between matrix A and matrix C?