If A = begin{bmatrix} 5 & 2 3 & 1 end{bmatri | vedclass

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(B) To find the inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,we use the formula $A^{-1} = \frac{1}{|A|} 	ext{a

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$\begin{bmatrix} -1 & 2 \ 3 & -5 \end{bmatrix}$

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(B) To find the inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,we use the formula $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$.Given $A = \begin{bmatrix} 5 & 2 \ 3 & 1 \end{bmatrix}$.First,calculate the determinant $|A| = (5)(1) - (2)(3) = 5 - 6 = -1$.Next,find the adjoint matrix $	ext{adj}(A)$ by swapping the diagonal elements and changing the signs of the off-diagonal elements: $	ext{adj}(A) = \begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix}$.Now,$A^{-1} = \frac{1}{-1} \begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix} = \begin{bmatrix} -1 & 2 \ 3 & -5 \end{bmatrix}$.Thus,the correct option is $B$.

If $A = \begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}$,then $A^{-1} = $

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