(Solved): Question 1 (a) Given: \( \quad \mathbf{A}=\left[\begin{array}{cc}1 & 0 \\ 3 & -5\end{array}\right] ...

Question 1 (a) Given: \( \quad \mathbf{A}=\left[\begin{array}{cc}1 & 0 \\ 3 & -5\end{array}\right] \) and \( \mathbf{B}=\left[\begin{array}{cc}-2 & 1 \\ 4 & -3\end{array}\right] \) Compute the following: (i) \( \mathrm{A}+\mathrm{B} \) [2 marks] (ii) \( 2 \mathrm{~A}-3 \mathrm{~B} \) [2 marks] (iii) \( \mathrm{AB} \) [2 marks] (iv) \( \mathrm{AB}+\mathrm{BA} \) [4 marks] (b) If \( A=\left[\begin{array}{cc}3 & 2 \\ -1 & 1\end{array}\right] \) and \( B=\left[\begin{array}{cc}0 & -4 \\ -2 & 8\end{array}\right] \), find matrices \( X \) such that \( 2 A+X=B \) [4 marks] (c) For the matrix \( A=\left[\begin{array}{ll}1 & 2 \\ 1 & 4\end{array}\right] \), find (i) \( \operatorname{det}(\mathrm{A}) \) (ii) \( A^{-1} \) [4 marks] (iii) \( X \) if \( A X=\left[\begin{array}{ll}5 & 6 \\ 7 & 2\end{array}\right] \) [Hint: multiply both side by \( A^{-1} \) ] [5 marks]