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

Options

A. `M^(2017)`
B. `M^(T)N`
C. `M^(2)N^(2)`
D. `MN`

Answer

A, B, C, D

Explanation

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`