If $A=\left[\begin{array}{cc}2 & -1 \ -1 & 2\end{array} ight]$ such that $A^2-4 A+3 I=0$, where $\mathrm{I}$ is a unit matrix of order 2 , then $A^{-1}$ is

Question

If $A=\left[\begin{array}{cc}2 & -1 \ -1 & 2\end{array}ight]$ such that $A^2-4 A+3 I=0$, where $\mathrm{I}$ is a unit matrix of order 2 , then $A^{-1}$ is

Aicharya · Accepted Answer

$\begin{aligned} & A^2-4 A+3 I=0 \Rightarrow A(4 I-A)=3 I \Rightarrow A\left(\frac{4 I-A}{3}ight)=I \ & \Rightarrow A^{-1}=\frac{4 I-A}{3}=\frac{1}{3}\left[\begin{array}{ll}2 & 1 \ 1 & 2\end{array}ight]\left[	ext { as } A A^{-1}=Iight]\end{aligned}$

If $A=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]$ such that $A^2-4 A+3 I=0$, where…

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