Step 1

To solve this problem, we use the standard result of matrix

Ans: We know that

\(det(A \cdot B)= det(A) \cdot det(B)\)

and

\(det(A)=det(A^T)\)\)

Step 2

Ans : Given that \(det(A)=2, det(B)=-2\)

\(det(ABA^T)=det(A) \cdot det(BA^T) \ \ \ \left\{det(A \cdot B)=det(A) \cdot det(B)\right\}\)

\(=det(A) \cdot det(B) \cdot det(A^T) \ \ \ \left\{det(A)=det(A^T)\right\}\)

\(=det(A) \cdot det(B) \cdot det(A)\)

\(=2 \cdot (-2) \cdot 2\)

\(det(ABA^T)=-8\)

To solve this problem, we use the standard result of matrix

Ans: We know that

\(det(A \cdot B)= det(A) \cdot det(B)\)

and

\(det(A)=det(A^T)\)\)

Step 2

Ans : Given that \(det(A)=2, det(B)=-2\)

\(det(ABA^T)=det(A) \cdot det(BA^T) \ \ \ \left\{det(A \cdot B)=det(A) \cdot det(B)\right\}\)

\(=det(A) \cdot det(B) \cdot det(A^T) \ \ \ \left\{det(A)=det(A^T)\right\}\)

\(=det(A) \cdot det(B) \cdot det(A)\)

\(=2 \cdot (-2) \cdot 2\)

\(det(ABA^T)=-8\)