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Question
`("aA")^-1 = 1/"a" "A"^-1`, where a is any real number and A is a square matrix.
Options
True
False
Solution
This statement is True.
Explanation:
If A is a non-singular square matrix, then for any non-zero scalar ‘a‘, aA is invertible.
∴ `("aA") * (1/"a" "A"^-1) = "a" * 1/"a" * "A" * "A"^-1` = I
So, (aA) is inverse of `(1/"a" "A"^-1)`
⇒ `("aA")^-1 = 1/"a" "A"^-1`
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