(MT)T = M
(cM)T = c(M)T
(M + N)T = MT + NT
MN = NM
Answer is Right!
Answer is Wrong!
The correct answer is D. MN = NM.
A. (MT)T = M is always true. This is because the transpose of a transpose is the original matrix.
B. (cM)T = c(M)T is always true. This is because the transpose of a scalar multiple is the scalar multiple of the transpose.
C. (M + N)T = MT + NT is always true. This is because the transpose of a sum is the sum of the transposes.
D. MN = NM is not always true. This is because the product of two matrices is not commutative, in general. For example, if $M = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $N = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$, then $MN = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$, but $NM = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$.