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  • Which of the following statements are True or False (AB)^-1 = A^-1.B^-1, where A and B are invertible matrices satisfying cumulative property with respect to multiplication.

Which of the following statements are True or False
(AB)^{-1} = A^{-1}.B^{-1}, where A and B are invertible matrices satisfying cumulative property with respect to multiplication.

Answers (1)

True

Given:

AB=BA

\begin{aligned} (A B)\left(A^{-1} B^{-1}\right) &=(B A)\left(A^{-1} B^{-1}\right) \\ &=B\left(A A^{-1}\right) B^{-1} \\ &=B \cdot I \cdot B^{-1}=B \cdot B^{-1}=I \\ (A B)^{-1} &=A^{-1} B^{-1} \end{aligned}

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infoexpert22

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