If `A=[[-a,b],[c,a]]` and `A^(2)=I`,then:

If A=[[-a,b],[c,d]] and A^(2)=I then

Let a,b,c in R be such that a+b+c gt 0 and abc = 2 . Let A = [(a,b,c),(b,c,a),(c,a,b)] If A^(2)=I then value of a^(3)+b^(3)+c^(3) is

If A_i= [ [a^i, b^i] , [b^i, a^i]] and if |a|<1, |b|<1 then sum_(i=1)^oo det(A_i) = (A) a^2/(1-a)^2- b^2/(1-b)^2 (B) a^2/(1-a)^2+ b^2/(1-b)^2 (C) a^2/(1+a)^2- b^2/(1+b)^2 (D) (a^2-b^2)/[(1-a^2)(1-b^2)]

If A=[1001],B=[100-1] and C=[0110], then show that A^(2)=B^(2)=C^(2)=I_(2)

If A=[[a+i b, c+i d],[-c+i d, a-i b]]a n da^2+b^2+c^2+d^2=1,t h e nA^(-1) is equal to a.[[a+i b,-c+i d],[-c+i d, a-i b]] b. [[a-i b,-c-i d],[-c-i d, a+i b]] c. [[a+i b,-c-i d],[-c+i d, a-i b]] d. none of these

If A=[(0,2b,c),(a,b,-c),(a,-b,c)] , then find the value of a, b and c. Such that A^(T)A=I

If A=[[0,1],[1,0]],B=[[0,-i],[i,0]] and C=[[i,0],[0,-i]] , show that A^2=B^2=-C^2=I_2 and AB=-BA,AC=-CA and BC=-CB .

If A = 1/ sqrt(3) [[1,1+i],[1-i,1]] then A(bar(A)^T) equals : a. O b. I c. -I d. 2I

Let a=i-2j+k" and "b=i-j+lambdak , (where lambda in Z ) be two vectors. If c is a vector such that a times b=c timesb, c*a=0" and "2b*c+1=0," then "lambda= ________

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .