If A = begin{bmatrix} a & c d & b end{bmatri | vedclass

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(A) The inverse of a matrix $A$ is given by the formula $A^{-1} = \frac{adj(A)}{|A|}$.First,we calculate the determinant of $A$:$|A| = \begin{vmatrix}

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$\frac{1}{ab - cd} \begin{bmatrix} b & -c \ -d & a \end{bmatrix}$

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(A) The inverse of a matrix $A$ is given by the formula $A^{-1} = \frac{adj(A)}{|A|}$.First,we calculate the determinant of $A$:$|A| = \begin{vmatrix} a & c \ d & b \end{vmatrix} = ab - cd$.Next,we find the adjoint of $A$ by swapping the diagonal elements and changing the signs of the off-diagonal elements:$adj(A) = \begin{bmatrix} b & -c \ -d & a \end{bmatrix}$.Therefore,$A^{-1} = \frac{1}{ab - cd} \begin{bmatrix} b & -c \ -d & a \end{bmatrix}$.

If $A = \begin{bmatrix} a & c \\ d & b \end{bmatrix}$,then $A^{-1} = $

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