If A and B are square matrices of order 3 such that A = 2 , B = 4 , then A a d j B = …

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Question: Answered & Verified by Expert

If A and B are square matrices of order 3 such that

|A| = 2, |B| = 4,

then

|A (a d j B)| =

…

MathematicsDeterminantsMHT CETMHT CET 2019 (Shift 1)

Options:

A 16
B 8
C 64
D 32

Solution:

1519 Upvotes Verified Answer

The correct answer is: 32

We have, A and B are square matrices of order 3 such that

|A| = 2, |B| = 4

Now,

|A (a d j) B| = |A| |a d j B| (∵ |A B| = |A| |B|)

|A| {|B|}^{3 - 1}

= |A| {|B|}^{2} = (2) {(4)}^{2} = 32

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