The inverse of the matrix A = begin{bmatrix} | vedclass

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(A) Step $1$: Find the determinant of $A$. $|A| = (3 	imes 4) - (-2 	imes 1) = 12 + 2 = 14$.Step $2$: Find the adjoint of $A$. For a $2 	imes 2$ ma

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$\begin{bmatrix} \frac{2}{7} & \frac{1}{7} \ -\frac{1}{14} & \frac{3}{14} \end{bmatrix}$

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(A) Step $1$: Find the determinant of $A$. $|A| = (3 	imes 4) - (-2 	imes 1) = 12 + 2 = 14$.Step $2$: Find the adjoint of $A$. For a $2 	imes 2$ matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$, the adjoint is $\begin{bmatrix} d & -b \ -c & a \end{bmatrix}$.Step $3$: Thus, $adj(A) = \begin{bmatrix} 4 & 2 \ -1 & 3 \end{bmatrix}$.Step $4$: The inverse is $A^{-1} = \frac{1}{|A|} adj(A) = \frac{1}{14} \begin{bmatrix} 4 & 2 \ -1 & 3 \end{bmatrix} = \begin{bmatrix} \frac{4}{14} & \frac{2}{14} \ -\frac{1}{14} & \frac{3}{14} \end{bmatrix} = \begin{bmatrix} \frac{2}{7} & \frac{1}{7} \ -\frac{1}{14} & \frac{3}{14} \end{bmatrix}$.

The inverse of the matrix $A = \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}$ is:

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