If `A=[(-1,1),(0,-2)]=B^3+C^3`, where B and C are 2 x 2 matrices with integer elements, then- `tr(B) - tr (C)` must be equal to

If A=[[-1,10,-2]]=B^(3)+C^(3), where B and c are 2x2 matrices with integer elements, then- tr(B)-tr(C) must be equal to

The number of 2xx2 idempotent matrices with integer entries are (A) 1 (B) 2 (C) 3 (D) oo

Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such that tr(A)=tr(B)=0then

If A , B and C are three square matrices of the same size such that B = CA C^(-1) then CA^(3) C^(-1) is equal to

If A and B are two matrices such that AB=A and BA=B, then B^(2) is equal to (a) B( b) A(c)1(d)0

Let A=[(1,0,3),(0,b,5),(-(1)/(3),0,c)] , where a, b, c are positive integers. If tr(A)=7 , then the greatest value of |A| is (where tr (A) denotes the trace of matric A i.e. the sum of principal diagonal elements of matrix A)

If A and B are two square matrices of the order 3, then the value of 998 tr(I)-999 tr(AB)+999tr (BA) is

Consider a matrix A=[(0,1,2),(0,-3,0),(1,1,1)]. If 6A^(-1)=aA^(2)+bA+cI , where a, b, c in and I is an identity matrix, then a+2b+3c is equal to

If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I , then tr. (A^(2)+B^(2)) is equal to ________.