If `213(-1 0-1-1 1 0 0 1 1)(1 0-1)=A ,` then write the order of matrix `A` .

If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A , then write the order of matrix A .

If [2 1 3] [{:(-1,0,-1),(-1,1,0),(0,1,1):}][{:(1),(0),(-1):}] =A, then find the value of A.

If A = [(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a null matrix (b) a unit matrix (c) A (d) A

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

If [(9,-1,4),(-2,1,3)]=A+[(1,2,-1),(0,4,9)], then find the matrix A.

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

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

If A^(-1)=[{:(,1,-1,0),(,0,-2,1),(,0,0,-1):}] then

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[[x,0, 0],[ 0,y,0],[ 0, 0,z]] , is (a) [[x^(-1),0 ,0 ],[0,y^(-1),0],[ 0, 0,z^(-1)]] (b) x y z[[x^(-1),0 ,0],[ 0,y^(-1),0],[ 0, 0,z^(-1)]] (c) 1/(x y z)[[x,0, 0],[ 0,y,0],[ 0, 0,z]] (d) 1/(x y z)[[1, 0, 0],[ 0 ,1, 0],[ 0, 0, 1]]

If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdotcdot[{:(1, n-1), (0,1):}] = [{:(1, 78), (0,1):}] , then the inverse of [{:(1, n), (0,1):}] is