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number of matrices in set s is equal to 6number of matrices in set S such that `|A-I_(2)| ne 0` is equal to 3 symmetric matrices are more than skew -symmetric matrices in set Sall matrices in set S are singular

Answer :

B::CSolution :

As, `A A^(T)=I_(2)` <br> `implies [[a,b],[c,d]],[[a,c],[b,d]]=[[1,0],[0,1]]` <br> `impliesa=0,b=pm1,d=0,c=pm1` <br> therefore Total 8 matrices are possible They are <br> `[[1,0],[0,1]],[[1,0],[0,-1]],[[-1,0],[0,1]],[[-1,0],[0,-1]]` <br> `[[0,1],[1,0]],[[0,-1],[1,0]],[[0,1],[-1,0]],[[0,-1],[-1,0]]` <br> Also `|A-I_(2)|=|A-A A^(T)|=|A||I_(2)-A^(T)|` <br> `=|A||(I_(2)-A^(T))^(T)|=|A||I_(2)-A|` <br> `=|A||A-I_(2)|` <br> `implies|A|=1(As,|A-I_(2)|ne 0)` <br> except `A=1=[[1,0],[0,1]]` <br> where `|A|=1 but` <br> `| A-I_(2)|=0` **Introduction and definition**

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