If A is a 2x2 matrix with real entries so that `A^(2)=3A-2I`, and p,q belongs to integers such that `A^(8)=pA+qI`, then p+q is

" If A is a "2times2" matrix with real entries so that "A^(2)=3A-2I," and "p,q" belongs to integers such that "A^(8)=pA+qI," then "p+q" is "

Let A be a 2 xx 2 real matrix with entries from { 0,1} and |A| ne 0 . Consider the following two statements : (P ) If A ne I_2 then |A| =-1 (Q ) if |A| =1 , then Tr (A)=2 Where I_2 denotes 2xx 2 identity matrix and tr (A) denotes the sum of the diagonal entries of A then :

If alpha,beta are the roots of the equation x^(2)+px-r=0 and (alpha)/(3),3 beta are the roots of the equation x^(2)+qx-r=0, then r equals (i)((3)/(8))(p-3q)(3p+q)(ii)((3)/(8))(3p-q)(3p+q)(iii)((3)/(64))(q-3p)(p-3p)(iv)((3)/(64))(p-q)(q-3p)

If p and q are positive real numbers such that p^2+q^2=1 , then the maximum value of p+q is

If a matrix A satisfies A^(2)-4A+3I=0 and if A^(8)=pA+qI ,then ((p)/(80)-40) equals

If p and q are distinct integers such that 2005 + p = q^2 and 2005 + q = p^2 then the product p.q is.

If p and q are positive real numbers such that p^(2)+q^(2)=1 then find the maximum value of (p+q)