If `A=[[0,a,b],[-a,0,c],[-b,-c,0]]`, find `1/2 (A+A\')` and `1/2 (A-A\')`

If A=[[1,0,0],[0,1,0],[a,b,-1]] , find A^2

If A=[[1, 1,-1],[ 2, 0, 3],[ 3,-1, 2]] , B=[[1, 3],[0,2],[-1, 4]] and C=[[1,2, 3,-4],[ 2, 0,-2, 1]] , find A(BC), (AB)C and show that (A B)C = A(B C) .

If A=[[0, 6, 7], [-6, 0, 8], [ 7,-8, 0]] , B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2, 0]] , C=[[2], [-2] , [3]] Calculate AC, BC and (A + B)C . Also, verify that (A + B)C = A C + B C

If A=[[1 ,2,-3],[ 5, 0, 2],[ 1,-1, 1]], B=[[3,-1, 2],[ 4, 2 ,5],[ 2, 0, 3]] and C=[[4, 1, 2],[ 0, 3, 2],[ 1,-2, 3]] , then compute (A+B) and (B - C) . Also, verify that A + (B - C) = (A + B) - C .

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

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

If A=[[0,1],[1,0]],B=[[0,-i],[i,0]] and C=[[i,0],[0,-i]] , show that A^2=B^2=-C^2=I_2 and AB=-BA,AC=-CA and BC=-CB .

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=I_2 .

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