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If A and B are square matrices of order 2 such that det (A B)= det (B A) , then which one of the following is correct?

Options

  1. AA must be a unit matrix.
  2. BB must be a unit matrix.
  3. CBoth A and B must be unit matrices.
  4. DA and B need not be unit matrices.

Correct answer

D. A and B need not be unit matrices.

Step-by-step solution

Let A= | array ll 2 & 0 0 & 2 array |_ 2 2 and B= | array ll 1 & 0 0 & 4 array |_ 2 2 aligned & |A|=4 and |B|=4 . & det (A B)= | array ll 2 & 0 0 & 2 array | | array ll 1 & 0 0 & 4 array |= | array ll 2 & 0 0 & 8 array |=16 aligned det (B A)= | array ll 1 & 0 0 & 4 array | | array ll 2 & 0 0 & 2 array |= | array ll 2 & 0 0 & 8 array |=16 Here det (A B)= det (B A) , but A and B are not unit matrices.

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