InterviewSolution
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InterviewSolution
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Let S be the set of 2xx2 matrices given by S={A=[[a,b],[c,d]],"where" a,b,c,d,in I},such that A^(T)=A^(-1) Then |
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Answer» number of matrices in set s is equal to 6 `implies [[a,b],[c,d]],[[a,c],[b,d]]=[[1,0],[0,1]]` `impliesa=0,b=pm1,d=0,c=pm1` therefore Total 8 matrices are POSSIBLE They are `[[1,0],[0,1]],[[1,0],[0,-1]],[[-1,0],[0,1]],[[-1,0],[0,-1]]` `[[0,1],[1,0]],[[0,-1],[1,0]],[[0,1],[-1,0]],[[0,-1],[-1,0]]` ALSO `|A-I_(2)|=|A-AA^(T)|=|A||I_(2)-A^(T)|` `=|A||(I_(2)-A^(T))^(T)|=|A||I_(2)-A|` `=|A||A-I_(2)|` `implies|A|=1(As,|A-I_(2)|ne 0)` except `A=1=[[1,0],[0,1]]` where `|A|=1 but` `| A-I_(2)|=0` |
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