JAMB 2002 · UME · Q36

If $N = \begin{pmatrix} 3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1 \end{pmatrix}$ , find $|N|$ .

Worked solution (try it first)

Expand along the first row, with signs $+ \; - \; +$ .
The first term is $3 \times ((-3)(1) - (-5)(2)) = 3 \times 7$
$= 21$ .
The second term is $-5 \times (6 \times 1 - (-5)(-2)) = -5 \times (-4)$
$= 20$ .
The third term is $-4 \times (6 \times 2 - (-3)(-2)) = -4 \times 6$
$= -24$ .
Add them: $21 + 20 - 24 = 17$ , option D.