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

Explanation:

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

This property is true regardless of whether A and B are unit matrices or not. Therefore, the condition det(AB) = det(BA) does not imply that either A or B must be a unit matrix.

∴ Option 4 is correct 

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.