If A and B are square matrices of the same or | vedclass

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(C) We are given the expression $(B^{-1}AB)^5$. This can be written as the product of $5$ terms: $(B^{-1}AB)^5 = (B^{-1}AB)(B^{-1}AB)(B^{-1}AB)(B^{-1}

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$B^{-1}A^5B$

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(C) We are given the expression $(B^{-1}AB)^5$. This can be written as the product of $5$ terms: $(B^{-1}AB)^5 = (B^{-1}AB)(B^{-1}AB)(B^{-1}AB)(B^{-1}AB)(B^{-1}AB)$. Since matrix multiplication is associative,we can group the terms as: $= B^{-1}A(BB^{-1})A(BB^{-1})A(BB^{-1})A(BB^{-1})AB$. Since $BB^{-1} = I$ (the identity matrix),the expression simplifies to: $= B^{-1}A(I)A(I)A(I)A(I)AB$. $= B^{-1}AAAAAB$. $= B^{-1}A^5B$.

If $A$ and $B$ are square matrices of the same order and $|B| \neq 0$,then $(B^{-1}AB)^5$ is equal to

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