If A and B are 4 times 4 matrices, det(A) = 1, det(B) = 4, then det(AB) = ? det(3A) = ? det(A^T) = ? det(B^{-1}) = ? det(B^4) = ?

Caelan 2020-11-07 Answered
If A and B are 4×4 matrices, det(A) = 1, det(B) = 4, then
det(AB) = ?
det(3A) = ?
det(AT)=?
det(B1)=?
det(B4)=?
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Expert Answer

Corben Pittman
Answered 2020-11-08 Author has 83 answers
Given that
A and B are 4×4 matrices:
det(A)=1 : det(B)=4 Then
(1) det(AB)=det(A)det(B)
=14
det(AB)=4
(2) det(3A)=3det(A)
=3(1)
det(3A)=3
(3) det(AT)=det(A)
det(AT)=1
(4)det(B1)=1|B|
det(B1)=14
(5) det(B4)=det(BBBB)
=det(B)det(B)det(B)det(B)
=4444
=256
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Jeffrey Jordon
Answered 2022-01-29 Author has 2087 answers

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