`A` is a `2xx2` matrix such that `A[[1],[-1]]=[[-1],[ 2]] and A^2[[1],[-1]]=[[1],[ 0]]dot` The sum of the elements of `A` is a.`-1` b. 0 c. 2 d. 5

If [[2,-1],[1,0],[-3,4]]A=[[-1,-8,-10],[1,-2,-5],[9,22,15]] , then sum of all the elements of matrix A is

Let M be a 3xx3 matrix satisfying M[[0], [1] ,[0]]=[[-1], [2], [3]] , M[[1],[-1], [0]]=[[1], [1],[-1]] ,and M[[1], [1], [1]]=[[0] ,[0], [12]] Then the sum of the diagonal entries of M is _________.

If A= [[3,-1],[1,2]],B=[[3],[1]],C=[[1],[-2]] find the matrix X such that AX = 3B+2C.

Let A +2B=[[1, 2, 0],[ 6,-3, 3],[-5, 3, 1] ] and 2A-B=[[2,-1, 5 ],[2,-1, 6],[ 0, 1, 2]] . Then T r(B) has the value equal to a. 0 b. 1 c. 2 d. none

If A = [[1,2],[3,-5]] and B=[[1,0],[0,2]] and X is a matrix such that A=BX , then X=

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i is a 2 xx 2 identity matrix, Tr(A) i= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2: |A| =1 . then (A) Statement 1 is false, statement 2 is true. (B) Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1. (C) Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1. (D) Statement 1 is true, statement 2 is false.

A is an involuntary matrix given by A=|[0, 1,-1], [4,-3, 4], [3,-3, 4]| , then the inverse of A//2 will be 2A b. (A^(-1))/2 c. A/2 d. A^2

Let a in (0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^2+.....+a^2007 Then sum of all possible values of S is a. 2010 b. 2009 c. 2008 d. 2

If A=[(0,1,2),(1,2,3),(3,1,1)] and its inverse B=[b_(ij)] , then the element b_(23) of matrix B is -

If A=[(1,0,2),(-1,1,-2),(0,2,1)]" and Adj "A=[(5,a,-2),(1,1,0),(-2,-2,b)] , then the values of a and b are -