Multiple choice

For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?

  1. (MT)T = M

  2. (cM)T = c(M)T

  3. (M+ N)T = MT + NT

  4. MN = NM
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$= \begin{bmatrix} \ n_1m_1 + n_2m_3 & n_1m_2 + n_2m_4 \ \ n_3m_1 + n_4m_3 & n_3m_2 + n_4m_4 \ \end{bmatrix} \\ MN \neq NM \\ \text{i.e. property does not hold always.}$

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