Verify that `A^(2)=I`, when `A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]`

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):}].

Verify : A(adj.A)=(adj.A)A=|A|I when : A=[{:(2,1,5),(3,-2,-4),(-3,1,-2):}]

Find the inverse following matrix and verify that A^(-1)A=I_3 . [(1, 3, 3),( 1, 4, 3),( 1, 3, 4)]

Verify : A(adj.A)=(adj.A)A=|A|I when : A=[{:(1,-1,2),(3,0,-2),(1,0,3):}]

Verify : A(adj.A)=(adj.A)A=|A|I when : A=[{:(1,2,3),(0,5,0),(2,4,3):}]

Verify (AB)^(-1)=B^(-1)A^(-1) with A=[{:(0,-3),(1,4)],B=[(-2,-3),(0,-1):}]

Verify that A(B+C)=AB+AC when A=[[4,-2] , [2,3]], B=[[-1,1,] , [3,-2]] and C=[[4,1] , [2,-1]]

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

Verify the following: (-1,2,1) , (1,-2,5) , (4,-7,8) and (2,-3,4) are the vertices of a parllelogram.

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