If $A = \begin{bmatrix} 2 & 1 & 0\\ 3 & 1 & 2 \\ 0 & 4 & -1\end{bmatrix}$ then |adj (A)| is equal to

225

$A = \begin{bmatrix} 2 & 1 & 0\\ 3 & 1 & 2 \\ 0 & 4 & -1\end{bmatrix}$

so A adj A = AI

so |A adj A| = |A|³

so |adj A| = |A|²

so finding |A| first

so $|A| = \begin{vmatrix} 1 & 2\\ 4 & -1 \end{vmatrix} -1\begin{vmatrix} 3 & 2\\ 0 & -1 \end{vmatrix} + 0$

= 2(-1 - 8) - 1(-3)

= 2(-9) + 3

= -18 + 3

= -15 = |A|

so |Adj A| = |A|² = (-15)²

= 225