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:

Question

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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).

Answer

Both Statement I and Statement II are correct

Answer

Both Statement I and Statement II are incorrect

Answer

Statement I is correct but Statement II is incorrect

Answer

Statement I is incorrect but Statement II is correct

	LIST I (Type of the Matrix)	LIST II (Property)
A.	Symmetric Matrix	I. a_ij = a_ji, for values of i and j
B.	Hermitian Matrix	II. a_ij = ā_ji, for values of i and j
C.	Skew-Hermitian matrix	III. a_ij = -ā_ji, for values of i and j
D.	Skew-Symmetric matrix	IV. a_ij = -a_ji, for values of i and j

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:

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The Correct Option is A

Solution and Explanation

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Statement (I): The determinant of a matrix A and its transpose AT 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: