If Mᵀ is the transpose of 2×2 matrix M, then which of the following is/are correct? I. |M + Mᵀ| = |M| + |Mᵀ| if M is symmetric. II. |M + Mᵀ| = 0 if M is skew-symmetric. Select the correct answer using the code given below:
A.I only
B.II only✓ Correct
C.Both I and II
D.Neither I nor II
Explanation
Statement I: If M is symmetric, M + Mᵀ = 2M, so |M + Mᵀ| = 4|M| (for 2×2). But |M| + |Mᵀ| = 2|M|. These are not equal in general, so I is false. Statement II: If M is skew-symmetric, then Mᵀ = −M, so M + Mᵀ = 0 (zero matrix), and |0| = 0. So II is true.
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