Answer
0
Work Step by Step
We are given:
$A=\begin{bmatrix}
1 & 2 & -1\\
2& 1 & 4
\end{bmatrix}$
$B=\begin{bmatrix}
2 & 1\\
5& -2\\
4 & 7
\end{bmatrix}$
then $BA=\begin{bmatrix}
4 & 5 & 2\\
1& 8 & -13 \\
18 & 15 & 24
\end{bmatrix}$
Hence here:
$\det(BA)=\begin{vmatrix}
4.8-5.1 & 5.(-13)-2.8\\
1.15-8.18 & 8.24-15(-13)
\end{vmatrix}=\begin{vmatrix}
27 & -81\\
-129& 387
\end{vmatrix}=27.387-(-129)(-81)=0$
