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

If A = [(0,0,0),(1,0,0),(0,1,0)] , verify that A^3 = O

Let A=[{:(2," "3,-1),(0,-5," "7):}] . Verify that (A')'=A.

If A=[{:(2,-3),(4," "5):}]" and "B=[{:(-1,2),(0,3):}] , find a matrix X such that A+2B+X=O.

If A=[ (3,-2),( 4 ,-2) ] and I=[(1,0),(0,1)] , then prove that A^2-A+2I=O .

If A=[{:(2,-1),(-1,2):}] , verify A^(2)-4A+3I=0 , where I=[{:(1,0),(0,1):}] and O=[{:(0,0),(0,0):}] . Hence find A^(-1) .

If P = (0,1,2) and Q = (4,-2,1), O = (0,0,0) then P hat O Q =

If A = [(1,-2),(3,0),(5,6)], B = [(0,-3, 4),(1,2,0)] , verify that (AB)' = B'A'

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

Let A = [(1,0),(2,3)], B = [(0,1,2),(3,2,1)] and C = [(1,0,4),(-2,1,0),(3,2,6)] . Verify that (AB) C = A (BC)

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