The matrix $A^2+4 A-5 I$, where $I$ is identity matrix and $A=\left[\begin{array}{cc}1 & 2 \ 4 & -3\end{array} ight]$, equals :

Question

The matrix $A^2+4 A-5 I$, where $I$ is identity matrix and $A=\left[\begin{array}{cc}1 & 2 \ 4 & -3\end{array}ight]$, equals :

Aicharya · Accepted Answer

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

The matrix $A^2+4 A-5 I$, where $I$ is identity matrix and $A=\left[\begin{array}{cc}1 & 2 \\ 4 &…

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