A,B,C are 3 times 3 matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is det(A^TA^{-1})?1-93-19

Bevan Mcdonald

Bevan Mcdonald

Answered question

2021-02-21

A,B,C are 3×3 matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is det(ATA1)?
1
-9
3
-1
9

Answer & Explanation

curwyrm

curwyrm

Skilled2021-02-22Added 87 answers

Step 1
Given that
A,B and C are 3×3 matrices.
To find
det(ATA1)
Step 2
Given that:
A,B,C are 3×3 matrices
det(A)=-3 , det(D)=-2, det(C)=6.
To find
det(ATA1)
We know that
det(AB)=detAdetB
det(A1)=1det(A)
det(AT)=det(A)
Hence consider
det(ATA1)
=det(AT)det(A1)
=det(A)1det(A)
=(3)13
=1
det(ATA1)=1
option A

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