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If M and N are orthogonal matrices of or...

If M and N are orthogonal matrices of order 3, then which of the following is (are) orthogonal matrix?

A

`M^(2017)`

B

`M^(T)N`

C

`M^(2)N^(2)`

D

`MN`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Given, `MM^(T)=I=M^(T)M`
`&" " N N^(T)=I=N^(T)N`
(A)Let `C=M^(2017)`
Now,`C C^(T)=MM…..MM^(T)M^(T)M^(T)…..M^(T)=1`
(B) Let `D =M^(T)N`
Now, `D D^(T)=M^(T)N(M^(T)N)^(T)`
`= M^(T)N N^(T)M = 1`
(C ) Let `P= M^(2)N^(2)=MMN N`
So, `P P^(T) = MMN N N^(T)N^(T)M^(T)M^(T)`
(D)Let `Q = MN implies Q Q^(T)=M N N^(T)M^(T)=I`
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