Which of the following is true for the matrix | vedclass

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(B) For any two invertible matrices $A$ and $B$ of the same order,the inverse of their product is given by the reversal law of inverses.We know that $

Vedclass · Accepted Answer

$(AB)^{-1} = B^{-1}A^{-1}$

Vedclass · Answer

(B) For any two invertible matrices $A$ and $B$ of the same order,the inverse of their product is given by the reversal law of inverses.We know that $(AB)(B^{-1}A^{-1}) = A(BB^{-1})A^{-1} = A(I)A^{-1} = AA^{-1} = I$.Similarly,$(B^{-1}A^{-1})(AB) = B^{-1}(A^{-1}A)B = B^{-1}(I)B = B^{-1}B = I$.Since $(AB)(B^{-1}A^{-1}) = I$ and $(B^{-1}A^{-1})(AB) = I$,it follows that $(AB)^{-1} = B^{-1}A^{-1}$.Therefore,option $B$ is correct.

Which of the following is true for the matrix product $AB$?

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