2 votes 2 votes 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 if $a=b \text{(or)} \theta =n\pi, \: n$ is an integer always never if $a\cos \theta \neq b\sin \theta$ Linear Algebra nielit2016mar-scientistc linear-algebra matrix + – admin asked Apr 2, 2020 retagged Oct 28, 2020 by Krithiga2101 admin 707 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply vg653 commented Apr 2, 2020 reply Follow Share A is the correct option. 0 votes 0 votes Vishal_kumar98 commented Nov 5, 2021 reply Follow Share https://gateoverflow.in/2735/Gate-cse-1996-question-2-6 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes option A will be correct. if a.b = b.a this is called commutative Vipin Tiwari answered Apr 3, 2020 Vipin Tiwari comment Share Follow See all 0 reply Please log in or register to add a comment.
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 DIBAKAR MAJEE answered May 30, 2020 DIBAKAR MAJEE comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes if a = b then commute property will satisfy Amit_k_Singh answered Nov 5, 2021 Amit_k_Singh comment Share Follow See all 0 reply Please log in or register to add a comment.