Question

If $A=\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$ and $B=\begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix},$ then the determinant value of $BA$ is

• A. $8$
• B. $0$
• C. $-8$
• D. $24$

Answer 1

Answer: (B)

$BA=\begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}=\begin{bmatrix} 17 & 22 & 27 \\ 22 & 29 & 36 \\ 27 & 36 & 45 \end{bmatrix}$
$\left|B A\right|=\begin{vmatrix} 17 & 5 & 5 \\ 22 & 7 & 7 \\ 27 & 9 & 9 \end{vmatrix}$ (Using $C_{3} \rightarrow C_{3}-C_{2}$ and $C_{2} \rightarrow C_{2}-C_{1}$ )
Hence, $\left|B A\right|=0$