Question

If the adjoint of a 3 $\times$ 3 matrix A is $\left[\begin{array}{ccc}1& 4& 4\\ 2& 1& 7\\ 1& 1& 3\end{array}\right]$ then the possible value (s) of the determinant of A is (are)

• A. 2
• B. -2
• C. 16
• D. -16

Answer 1

Answer: (A), (B)

The correct options are
A 2
B -2

AdJ A = $\left[\begin{array}{ccc}1& 4& 4\\ 2& 1& 7\\ 1& 1& 3\end{array}\right]$
$|AdJA|=4=|A{|}^2\therefore |A|=\pm 2$