If `X` is a `2 xx 3` matrix such that `|X' X|!=0` and `A = I_2 - X(X' X)^(-1) X',` then `A^2` is equal to

If A={:((1,2),(3,4)):} and X is a 2 xx2 matrix such that AX = I , find X.

If A = [[1,2],[3,4]] and X is a 2xx2 matrix such that AX = I , then find X .

If A=[(x,1),(1,0)] and A^(2) is the identity matrix, then x is equal to

If A = [{:(1,2),(0,3):}] is a 2 xx 2 matrix and f(x) = x^(2) - x + 2 is a polynomial, then what is f (A) ?

If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int_(1//x)^(x) f(t)dt, (1)/(2) le x le 2x , then I is equal to

If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int_(1//x)^(x) f(t)dt, (1)/(2) le x le 2x , then I is equal to

I = int (x + x^(2/3) + x^(1/6))/(x (1+x^(1/3))) dx is equal

Let f(x)=(1+2x)(1+2x+4x^(2)+8x^(3)+...oo) If A is a matrix for which A^(3)=0, then f(A) equals (I is identity matrix of order equivalent to order of A).