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

If A and B are square matrices of order 2 such that det(AB) = det(BA), then which one of the following is correct? Correct Answer Both A and B must be unit matrices.

Explanation:

If A and B are square matrices of order 2 such that det(AB) = det(BA)

Only possible when A and B must be the Unit Matrix.

Additional Information Properties of determinants:

  • The determinant of a diagonal matrix is the product of the diagonal entries.
  • If A and B are both n×n matrices, then det(AB) = det(A) det(B).
  • For a n×n matrix A, det(kA) = kn det(A).

  • The determinant of a square matrix is the same as the determinant of its transpose.

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