Verify that `A(B+C)=(AB+AC),` when
(i) `A=[{:(1,2),(3,4):}],B=[{:(2," "0),(1,-3):}]" and "C=[{:(1,-1),(0," "1):}].`
(ii) `A=[{:(2,3),(-1,4),(0,1):}],B=[{:(5,-3),(2," "1):}]" and "C=[{:(-1,2),(" "3,4):}].`

For the following matrices, verify that A(BC)=(AB)C : (i) A=[{:(1,2,5),(0,1,3):}],B=[{:(2," "3,0),(1," "0,4),(1,-1,2):}]" and "C=[{:(1),(4),(5):}] (ii) A=[{:(2,3,-1),(3,0," "2):}],B=[{:(1),(1),(2):}]" and "C=[1-2]

If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}] and C=[{:(1,0),(-1,0):}] , verfity (i) A(B+C)=AB+AC.

For each of the following pairs of matrices A and B, verify that (AB)'=(B'A'): (i) A=[{:(1,3),(2,4):}]" and "B=[{:(1,4),(2,5):}] (ii) A=[{:(3,-1),(-2,-2):}]" and "B=[{:(1,-3),(2,-1):}] A=[{:(-1),(2),(3):}]" and "B=[-2" "-1" "-4] (iv) A=[{:(-1," "2,-3),(4,-5," "6):}]" and "B=[{:(" "3,-4),(" "2," "1),(-1," "0):}]

if A=[(1,2),(3,4):}],B=[{:(-1,0),(2,3):}]and C=[{:(1,-1),(0,1):}], then show that : (i) A(B+C)=AB+AC (ii) (A-B)C=AC-BC.

If A=[(-1,0,2),(3,1,4)], B=[(0,-2,5),(1,-3,1)] and C=[(1,-5,2),(6,0,-4)], then find (2A-3B+4C).

If A=[{:(3,2),(1,0):}],B=[{:(1,-2,5),(0,7,3):}]" and "C=[{:(8,1,-6),(2,-5,0):}] , verify that A(B+C)=(AB+AC).

If A = [{:(2, -3), (4, 1):}], B = [{:(2, 3), (5, 0):}]" and " C = [{:(-1, 2),(0, 5):}] then find A(B + C).

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):}]

Let A=[{:(0,1,-2),(5,-1,-4):}],B=[{:(1,-3,-1),(0,-2," "5):}]" and "C=[{:(2,-5,1),(-4," "0,6):}]. Compute 5A-3B+4C.