Show that `A B!=B A` in each of the following cases: `A=[5-1 6 7]` and `B=[2 1 3 4]` (ii) `A=[-1 1 0 0-1 1 2 3 4]` and `B=[1 2 3 0 1 0 1 1 0]` (iii) `A=[1 3 0 1 1 0 4 1 0]` and `B=[0 1 0 1 0 0 0 5 1]`

Evaluate the following: ([1 3-1-4]+[3-2-1 1])[1 3 5 2 4 6] (ii) [1 2 3][1 0 2 2 0 1 0 1 2][2 4 6] (iii) [1-1 0 2 2 3]([1 0 2 2 0 1]-[0 1 2 1 0 2])

For the following matrices verify the associativity of matrix multiplication i.e. (A B)C=A(B C)dot A=[1 2 0-1 0 1] , B=[1 0-1 2 0 3] and C=[1-1] (ii) A=[4 2 3 1 1 2 3 0 1] , B=[1-1 1 0 1 2 2-1 1] and C=[1 2-1 3 0 1 0 0 1] .

if A = [[-1, 1 ],[0 ,4 ]] and B = [ [ -3 , 2 ] , [ 0 ,-1 ] ] then show that ( A + B )^2

If A=[[1, 0, 1], [0, 2, 3], [1, 2, 1]], b=[[1, 2, 3], [1, 1, 5], [2, 4, 7]] and XA=B , then X=

If A=[[-2, 0, 0], [-2, -1, 3]], B=[[0, 1], [2, 3], [1, -1]] , then

Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]] (ii) [[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]!=[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]

Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]

Let A d+2B=[1 2 0 6-3 3-5 3 1]a n d2A-B=[2-1 5 0-1 6 0 1 2] . Then T r(B) has the value equal to 0 b. 1 c. 2 d. none

Find AB if A = [{:( 2,1,3),( 2, 9, 2 ),( 7, 4 , 3):}] and B = [{:( 1, 0 , 0),( 0,0,1),(0, 1, 0):}]

If A = [[-1, 2 ,3],[-1, 0, 2],[1, -3, 1]] and B = [[4,5,6],[-1, 0, 1], [2,1,2]], find 4A-3B