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The matrices $\begin{bmatrix} \cos\theta  &-\sin \theta  \\  \sin \theta & cos \theta \end{bmatrix}$ and  $\begin{bmatrix} a & 0  \\  0 & b \end{bmatrix}$ commute under the multiplication

  1. if $a=b \text{(or)} \theta =n\pi, \: n$ is an integer
  2. always
  3. never
  4. if $a\cos \theta \neq b\sin \theta$
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2 Comments

A is the correct option.
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3 Answers

1 vote
1 vote
option A will be correct.

if a.b = b.a

this is called commutative
0 votes
0 votes
option A is correct.

It can be shown by multiplication Row x Column wise.and to bring the same result i.e commutative either a=b or theta = n*pie
0 votes
0 votes

 if a = b then commute property will satisfy

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