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

Question

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

Aicharya · Accepted Answer

$A=\left[\begin{array}{cc}2 & -1 \ -1 & 2\end{array}ight] \quad \Rightarrow|A|=4-1=3 \quad$ and $(\operatorname{adj} A)=\left[\begin{array}{ll}2 & 1 \ 1 & 2\end{array}ight]$ $	herefore A^{-1} \quad=\frac{1}{3}\left[\begin{array}{ll}2 & 1 \ 1 & 2\end{array}ight]$

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

Solution