Verify that A^2= I when A= [ ll 5 & -4 6 & -5 ] - Vidyadip

Question

Verify that $A^2=$ I when $A=\left[\begin{array}{ll}5 & -4 \\ 6 & -5\end{array}\right]$

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Answer

$\begin{aligned} & A=\left[\begin{array}{ll}5 & -4 \\ 6 & -5\end{array}\right] \\ & A^2=\left[\begin{array}{ll}5 & -4 \\ 6 & -5\end{array}\right] \times\left[\begin{array}{ll}5 & -4 \\ 6 & -5\end{array}\right] \\ & =\left[\begin{array}{ll}25-24 & -20+20 \\ 30-30 & -24+25\end{array}\right] \\ & =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=I \\ & A^2=\text { I } \\ & \therefore \text { L.H.S. }=\text { R.H.S. }\end{aligned}$

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