1.If `A=[[1,0],[2,-1]], B=[[3,7],[4,8]], C=[[-1,1],[0,0]],` then prove that `A+(B+C)=(A+B)+C`

If =[[2,3],[4,5]],B=[[3,4],[7,2]], C=[[1,0],[0,7]] then verify that (AB)C=A(BC)

If A=[[1,0],[0,1]],B=[[1,0],[0,-1]] and C=[[0,1],[1,0]] then show that A^(2)=B^(2)=C^(2)

If A = [[2,3],[-1,5]] , B = [[3,-1],[4,7]] and C = [[5,-1],[0,3]], show that A(B +C)=AB+AC

If A=[[1,0,5],[3,2,7],[5,4,8]],B=[[3,1,2],[9,0,-6],[7,4,1]],C=[[2,0,-1],[7,5,6],[1,1,4]] , verify that A+(B+C)=(A+B)+C

If A=[[2,3,4],[-3,0,2]], B=[[3,-4,-5],[1,2,1]] and C=[[5,-1,2],[7,0,3]] , find the matrix X such that 2A+3B=X+C

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

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=[[3,9,0],[1,8,-2]] and B=[[4,0,2],[7,1,4]] ,find A+B and A-B .

If A=[[1,0,1],[0,2,0],[1,-1,4]],A=B+C,B=B^(T) and C=-C^(T) , then C=

If A=[(2,3,4),(-3,0,2)], B=[(3,-4,-5),(1,2,1)], C=[(5,-1,0),(7,0,3)], then find A+B+C.