If M^ T is the transpose of a 2 2 matrix M, then which of the following is/are correct ? I. |M+M^ T |=|M|+|M^ T | if M is symmetric. II. |M+M^ T |=0 if M is anti-symmetric. Select the answer using the code given below :

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Correct answer: B. II only

For Statement I: If M is a symmetric matrix of order 2 2, then M^ T = M. |M+M^ T | = |2M| = 2^2|M| = 4|M| |M| + |M^ T | = |M| + |M| = 2|M| Since 4|M| 2|M| for all symmetric matrices, Statement I is incorrect. For Statement II: If M is an anti-symmetric matrix, then M^ T = -M. M+M^ T = M - M = O |M+M^ T | = |O| = 0 Statement II is correct. Answer: II only

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