If `A=[[0,0],[0,1]]` ,then the matrix,given by `B=I+A+A^(2)+.......A^(K)` ,is

If A= [[0,0],[0,1]] then the matrix, given by B = 1 + A+ A^(2)+.......A^(k) , is

If A=[{:(0,1),(1,0):}] then the matrix A is

If A = [{:(0,1),(1,0):}] , then the matrix A is/an

Let A be a square matrix satisfying two conditions (i) A^(k)=0,k in N (ii) If A^(l)=0 for some l in N, then I>=k. Prove that (I-A) is invertible and its inverse is given by B=I+A+A^(2)+......+A^(k-1)

Let matrix A=[[1,0,0],[1,0,1],[0,1,0]] then the value of |A^(2012)-I| is equal to

Let I = [{:(1, 0, 0),(0 ,1, 0),(0,0,1):}] and P = [{:(1, 0, 0),(0 ,-1, 0),(0,0,-2):}] . Then the matrix p^(3) + 2P^(2) is equal to

If A = [(2,0),(0,1)] and B = [(1),(2)] then find the matrix X such that A^(-1) X = B

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisgying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The ratio of the trace of the matrix B to the matrix C, is

If A = [[0,1],[0,0]], I is the unit null matrix of order 2 and a,b are arbitrary constants, then (aI+bA)^2 is equal to

If A= [{:(2, -5), (0, 1):}]" and I" = [{:(1, 0), (0, 1):}] then find the matrix X such that 4A-2X + I = O.