Question

If A is a non-singular matrix, then which of the following is not true?

Options

• adj A is singular

• (adj A)⁻¹ = (adj A⁻¹)

• |A| ≠ 0

• A⁻¹ exists

Answer 1

adj A is singular

Explanation:

The determinant of an adjoint matrix is given by the formula |adj A| = |A|ⁿ⁻¹. Since |A| ≠ 0, it follows that |adj A| ≠ 0. Thus, Adj A must also be non-singular.