Question

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

• A. \( \text{adj } A \) is singular
• B. \( (\text{adj } A)^{-1} = (\text{adj } A^{-1}) \)
• C. \( |A| \neq 0 \)
• D. \( A^{-1} \) exists

Hint:

If a matrix \( A \) is invertible (non-singular), all related structural matrices such as \( A^{-1} \), \( \text{adj } A \), and \( A^T \) are also fully invertible (non-singular).

Answer 1

The Correct Option is A