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

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

Let A=[{:(3," "4),(-2," "0),(7,-5):}]" and "B=[{:(2,-3),(5," "6),(-1," "8):}]. Verify that (A+B)'=A'+B'.

IF A=[{:(2,-1,2),(1,3,-4):}] and B=[{:(1,-2),(-3,0),(5,4):}] then verify that (AB)'=B'A'.

If A'=[{:(3,4),(-1,2),(0,1):}] and B=[{:(-1,2,1),(1,2,3):}] then verify that (A+B)'=A'+B'.

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

If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify that (i) (A')'=A (ii) (AB)'=B'A'

If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify that (i) (A')'=A (ii) (AB)'=B'A'

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

Let A = [(1,-2,3), (0,4,7)] and B = [(0,4,2),(2,-2,1)] verify that (A + B)^t = A ^t + B^t

If A = [(2,-1,2),(1,3,-4)], and B = [(1,-2),(-3,0),(5,4)] then verify that (AB)' = B'A'.