" 1.If "A=[[1,2,2],[2,1,2],[2,2,1]]" ,verify that "A^(2)-4A-51=0

If A=[[1,2,2],[2,1,2],[2,2,1]] , verify that : A^2-4A-5I=O

If A= [[1,2,2,],[2,1,2,],[2,2,1,]] then verify A^-1A=I

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],[0,-2,3]] verify that A(B+C)=AB+AC

If A=[[2,-1, 1],[-1 ,2,-1],[ 1, 1, 2]] .Verify that A^3-6A^2+9A-4I=0 and hence find A^(-1) .

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

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

If A = [[3,sqrt3,2],[4,2,0] and B = [[2,-1,2],[1,2,4]] , verify that : (A')'=A

If A=[[2,-1],[3,-2],[4,1]] and B=[[0,3,-4],[2,-1,1]] ,verify that (AB)^T=B^TA^T

If A=[[2,-1],[3,-2],[4,1]] and B=[[0,3,-4],[2,-1,1]] ,verify that (BA)^T=A^TB^T

If A=[(2,1),(1,0)],B=[(1,-1),(2,3)] , verify that : (A+B)^(2)!=A^(2)+2AB+B^(2)