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]`

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 0-2 3-1 0-2 1 1] , B=[0 5-4-2 1 3-1 0 2] and C=[1 5 2-1 1 0 0-1 1] , verify that A(B-C)=A B-A Cdot

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]]

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):}]

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):}]

Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[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]] ne[[(-1), 1, 0],[ 0, (-1), 1],[ 2, 3, 4]] [[1 , 2, 3],[ 0, 1, 0],[ 1, 1, 0]] .

Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Find AB

Compute AB and BA, whichever exists when (i) A=[{:(2,-1),(3," "0),(-1," "4):}]" and "B=[{:(-2,3),(0,4):}] (ii) A=[{:(-1,1),(-2,2),(-3,3):}]" and "B=[{:(" "3,-2," "1),(" "0," "1," "2),(-3," "4,-5):}] (iii) A=[{:(0,1,-5),(2,4," "0):}]" and "B=[{:(1,3),(-1,0),(0,5):}] (iv) A=[1" "2" "3" "4]" and "B=[{:(1),(2),(3),(4):}] (v) A=[{:(2,1),(3,2),(-1,1):}]" and "B=[{:(1,0,1),(-1,2,1):}]

" (b) Find the rank of the matrix : "A=[[2,1,4,7],[3,6,2,1],[0,0,1,5]]