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
48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z"/> Subscribe on YouTubeB. (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 $NM = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$.