Questions
Suppose A and B are two orthogonal matrices of the same size such that then
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a
A + B = –I
b
A + B = I
c
det(A+B)=0
d
A + B =O
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Correct option is C
As A, B are orthogonal matrices, AA′=BB′=I, det(A)≠0,det(B)≠0. Let C=A+B C′=A′+B′⇒AC′=AA′+AB′=I+AB′⇒AC′B=B+AB′B=B+ANow, det(A+B)=detAC′B=det(A)detC′det(B) =det(A)det(C)(−det(A))⇒ det(C)=−(det(A))2det(C)=−det(C)⇒ det(C)=0Similar Questions
Suppose .Product of zeros of is
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