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Question
(AB)–1 = A–1. B–1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.
Options
True
False
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Solution
This statement is True.
Explanation:
If A and B are invertible matrices of the same order
∴ (AB)–1 = (BA)–1 ......[∵ AB = BA]
But (AB)–1 = A–1B–1
∴ (BA)–1 = B–1A–1
So A–1B–1 = B–1A–1
∴ A and B satisfy commutative property w.r.t. multiplication.
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