If A is a 2 times 2 order non-singular matrix | vedclass

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(B) We know that for any non-singular matrix $A$,the product of $A$ and its inverse $A^{-1}$ is the identity matrix $I$. $A \cdot A^{-1} = I$ Taking t

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$\frac{1}{\det(A)}$

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(B) We know that for any non-singular matrix $A$,the product of $A$ and its inverse $A^{-1}$ is the identity matrix $I$. $A \cdot A^{-1} = I$ Taking the determinant on both sides: $\det(A \cdot A^{-1}) = \det(I)$ Using the property $\det(AB) = \det(A) \cdot \det(B)$,we get: $\det(A) \cdot \det(A^{-1}) = \det(I)$ Since $\det(I) = 1$ for an identity matrix,we have: $\det(A) \cdot \det(A^{-1}) = 1$ Therefore,$\det(A^{-1}) = \frac{1}{\det(A)}$.

If $A$ is a $2 \times 2$ order non-singular matrix,then the determinant of $A^{-1}$ is . . . . . . .

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