If A = begin{bmatrix} 2 & -1 -1 & 2 end{bmat | vedclass

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(C) Given the equation $A^2 - 4A + 3I = 0$.Subtract $3I$ from both sides: $A^2 - 4A = -3I$.Multiply by $A^{-1}$ on both sides: $A^{-1}(A^2 - 4A) = A^{

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$\frac{1}{3} \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix}$

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(C) Given the equation $A^2 - 4A + 3I = 0$.Subtract $3I$ from both sides: $A^2 - 4A = -3I$.Multiply by $A^{-1}$ on both sides: $A^{-1}(A^2 - 4A) = A^{-1}(-3I)$.This simplifies to $A - 4I = -3A^{-1}$.Therefore,$A^{-1} = -\frac{1}{3}(A - 4I) = \frac{1}{3}(4I - A)$.Substitute $A = \begin{bmatrix} 2 & -1 \ -1 & 2 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$:$A^{-1} = \frac{1}{3} \left( \begin{bmatrix} 4 & 0 \ 0 & 4 \end{bmatrix} - \begin{bmatrix} 2 & -1 \ -1 & 2 \end{bmatrix} ight) = \frac{1}{3} \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix}$.

If $A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$ such that $A^2 - 4A + 3I = 0$,where $I$ is a unit matrix of order $2$,then $A^{-1}$ is

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