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Let A and B be (3 xx 3) matrices with de...

Let A and B be (3 `xx` 3) matrices with det A = 4 and det B = 3.
What is det (3 `AB^(-1)`)equal to ?

A

12

B

18

C

36

D

48

Text Solution

Verified by Experts

The correct Answer is:
C
`det(3AB^(-1))=(3)^(3)|A||B^(-1)|`
` =27(|A|)/(|B|)=overset(9)cancel(27)xx(4)/(underset(1)cancel(3))=36`
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