A,B,C are 3 times 3 matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is det(A^2BC^{-1})? -3 -18 18 -108 36

UkusakazaL 2020-11-10 Answered
A,B,C are 3×3 matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is det(A2BC1)?
-3
-18
18
-108
36
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Expert Answer

Delorenzoz
Answered 2020-11-11 Author has 91 answers
Step 1
Given A, B and C are 3×3 matrices.
and
|A|=3
|B|=2
|C|=6
Find the determinant of (A2BC1)
Step 2
since,
|AB|=|A||B|
|An|=|A|n
and
|A1|=1|A|
Then,
|A2BC1|=|A2||B||C1|
=|A2||B|×1|C|
Substitute all the given values,
Step 3
|A2BC1|=(3)2(2)×16
=9×(2)×16
=18×16
=3
Hence,
|A2BC1|=3
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