Question

Statement (I): The determinant of a matrix A and its transpose A^T are equal.
Statement (II): The determinant of the product of two matrices A and B is the product of their determinants.
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

Both properties of determinants are standard facts and hold for any square matrices.

Answer 1

The Correct Option is A

Statement (I) is true because the determinant of a matrix and its transpose are always equal. Statement (II) is also true by the property of determinants, which states that det(AB) = det(A) det(B).