Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& {\mathrm{A}}^2+4\mathrm{A}-5\mathrm{I}=\mathrm{A}\times \mathrm{A}+4\mathrm{A}-5\mathrm{I}\\ =& \left[\begin{array}{cc}1& 2\\ 4& -3\end{array}\right]\times \left[\begin{array}{cc}1& 2\\ 4& -3\end{array}\right]+4\left[\begin{array}{cc}1& 2\\ 4& -3\end{array}\right]-5\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right]\\ & =\left[\begin{array}{cc}9& -4\\ -8& 17\end{array}\right]+\left[\begin{array}{cc}4& 8\\ 16& -12\end{array}\right]-\left[\begin{array}{cc}5& 0\\ 0& 5\end{array}\right]\\ & =\left[\begin{array}{cc}9+4-5& -4+8-0\\ -8+16-0& 17-12-5\end{array}\right]=\left[\begin{array}{ll}8& 4\\ 8& 0\end{array}\right]\\ & =4\left[\begin{array}{ll}2& 1\\ 2& 0\end{array}\right]\end{array}$