If M^ T is the transpose of a 2×2 matrix M , then which of the...

For Statement I:

If $M$ is a symmetric matrix of order $2 \times 2$, then $M^{\text{T}} = M$.

$|M+M^{\text{T}}| = |2M| = 2^2|M| = 4|M|$

$|M| + |M^{\text{T}}| = |M| + |M| = 2|M|$

Since $4|M| \neq 2|M|$ for all symmetric matrices, Statement I is incorrect.

For Statement II:

If $M$ is an anti-symmetric matrix, then $M^{\text{T}} = -M$.

$M+M^{\text{T}} = M - M = O$

$|M+M^{\text{T}}| = |O| = 0$

Statement II is correct.

Answer: II only