Question

`("aA")^-1 = 1/"a"  "A"^-1`, where a is any real number and A is a square matrix.

Options

• True

• False

Answer 1

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`