Find the inverse of the matrix A = left[begin | vedclass

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(A) Given matrix $A = \left[\begin{array}{cc}2 & -3 \ -1 & 2\end{array}ight]$.First,calculate the determinant $|A| = (2)(2) - (-3)(-1) = 4 - 3 = 1$

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$A^{-1} = \left[\begin{array}{cc}2 & 3 \ 1 & 2\end{array}ight]$

Vedclass · Answer

(A) Given matrix $A = \left[\begin{array}{cc}2 & -3 \ -1 & 2\end{array}ight]$.First,calculate the determinant $|A| = (2)(2) - (-3)(-1) = 4 - 3 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The formula for the inverse of a $2 	imes 2$ matrix $\left[\begin{array}{cc}a & b \ c & d\end{array}ight]$ is $\frac{1}{ad-bc} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Applying this to matrix $A$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}2 & 3 \ 1 & 2\end{array}ight] = \left[\begin{array}{cc}2 & 3 \ 1 & 2\end{array}ight]$.

Find the inverse of the matrix $A = \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,if it exists.

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