Answer
15876
Work Step by Step
We are given:
$A=\begin{bmatrix}
1 & 2 & -1\\
2& 1 & 4
\end{bmatrix}$
$\rightarrow A^T=\begin{bmatrix}
1 &2 \\
2& 1 \\
-1 & 4
\end{bmatrix}$
then $\rightarrow AA^T=\begin{bmatrix}
6 &0 \\
0& 21
\end{bmatrix}$
Find the determinants of $AA^T$
$\det(AA^T)=6.21-0=126$
Hence here:
$\det((AAT)^2) =[\det(AA^T)][\det(AA^T)]=126.126=15876$
