If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det (ABA^T) = ???

If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det$\left(AB{A}^{T}\right)=???$

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Step 1
To solve this problem, we use the standard result of matrix
Ans: We know that
$det\left(A\cdot B\right)=det\left(A\right)\cdot det\left(B\right)$
and
$det\left(A\right)=det\left({A}^{T}\right)$
Step 2
Ans : Given that $det\left(A\right)=2,det\left(B\right)=-2$

$=det\left(A\right)\cdot det\left(B\right)\cdot det\left(A\right)$
$=2\cdot \left(-2\right)\cdot 2$
$det\left(AB{A}^{T}\right)=-8$

Jeffrey Jordon