If A and B are two invertible square matrices of same order, then what is ( AB ) − 1 equal to?

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Question: Answered & Verified by Expert

If $\mathrm{A}$ and $\mathrm{B}$ are two invertible square matrices of same order, then what is $(\mathrm{AB})^{-1}$ equal to?

MathematicsMatricesNDANDA 2018 (Phase 2)

Options:

A $\mathrm{B}^{-1} \mathrm{~A}^{-1}$
B $\mathrm{A}^{-1} \mathrm{~B}^{-1}$
C $\mathrm{B}^{-1} \mathrm{~A}$
D $\mathrm{A}^{-1} \mathrm{~B}$

Solution:

2419 Upvotes Verified Answer

The correct answer is: $\mathrm{B}^{-1} \mathrm{~A}^{-1}$

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

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