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:

Question

Accepted Answer

II only. If M is symmetric, M^T = M, so M + M^T = 2M and |2M| = 4|M|, but |M| + |M^T| = 2|M|, so statement I is false in general. If M is anti-symmetric, M^T = -M, so M + M^T = 0 matrix, hence |M + M^T| = 0. So only statement II is correct.

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:

Explanation

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