Given A and C are involutory matrices and B i | vedclass

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(D) We are given that $A$ and $C$ are involutory matrices,which means $A^2 = I$ and $C^2 = I$. This implies $A^{-1} = A$ and $C^{-1} = C$. Using the p

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$CBA$

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(D) We are given that $A$ and $C$ are involutory matrices,which means $A^2 = I$ and $C^2 = I$. This implies $A^{-1} = A$ and $C^{-1} = C$. Using the property of matrix inversion $(XYZ)^{-1} = Z^{-1}Y^{-1}X^{-1}$,we have: $(AB^{-1}C)^{-1} = C^{-1}(B^{-1})^{-1}A^{-1}$. Since $(B^{-1})^{-1} = B$,we get: $(AB^{-1}C)^{-1} = C^{-1}BA^{-1}$. Substituting $C^{-1} = C$ and $A^{-1} = A$,we obtain: $(AB^{-1}C)^{-1} = CBA$.

Given $A$ and $C$ are involutory matrices and $B$ is a non-singular matrix,then $(AB^{-1}C)^{-1}$ is equal to -

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