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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` |
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Answer» Correct Answer - 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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