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  4. If A and B are square matrices and A -1 and B-1 of the same order exist, then (AB)-1 is equal to :

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Q. If A and B are square matrices and $A^{ -1}$ and $B^{-1}$ of the same order exist, then $(AB)^{-1}$ is equal to :

Determinants

Solution:

Let A and B be square matrices and $A^{-1},B^{-1}$ be of same order.
then $(AB)^{-1} = B^{-1}. A^{-1}$.