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

Tazmin Horton 2020-11-07 Answered

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

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Expert Answer

FieniChoonin
Answered 2020-11-08 Author has 102 answers

Step 1
To solve this problem, we use the standard result of matrix
Ans: We know that
det(AB)=det(A)det(B)
and
det(A)=det(AT)
Step 2
Ans : Given that det(A)=2,det(B)=2
det(ABAT)=det(A)det(BAT)   {det(AB)=det(A)det(B)}
=det(A)det(B)det(AT)   {det(A)=det(AT)}
=det(A)det(B)det(A)
=2(2)2
det(ABAT)=8

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Jeffrey Jordon
Answered 2022-01-27 Author has 2495 answers

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