The GATE Grind

GATE 2014 EC (EC1) – Question 11

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

For same-dimension matrices M,N and scalar c, which property does NOT always hold?

  1. $(M^T)^T=M$
  2. $(cM)^T=cM^T$
  3. $(M+N)^T=M^T+N^T$
  4. $MN=NM$

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Show answer and explanation

Correct answer: (D) $MN=NM$

Explanation

Matrix multiplication is associative and distributes over addition, but does not generally commute. For example, let A have only entry A12=1 and B have only B21=1. Then AB has entry11=1 whereas BA has entry22=1. Thus the proposed equality AB=BA is false in general, **D**.