1.If A = `[[0,1,-1],[3,-2,3],[2,-2,3]]`. Show that` A^2 = 1` .

If A=[[4,-1,-4],[ 3, 0,-4],[ 3,-1,-3]] , show that A^2=I_3dot

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

If A=[[1,2,3],[0,1,0],[1,1,0]] and B=[[-1,1,0],[0,-1,1],[2,3,4]] show that AB!=BA

If A=[[3, 1],[-1, 2]] , show that A^2-5A+7I=0

If A=[(1,2),(2,1)] show that A^(2)-3I=2A

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=[[0 ,1 ,3],[ 1, 2,x],[2, 3, 1]] and A^(-1)=[[1//2,-4 ,5//2],[-1//2, 3,-3//2],[ 1//2,y,1//2]] ,find x ,\ y .

If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I^2=O .

If A=|{:(1,1,1),(1,2,-3),(2,-1,3):}| , then show that A. (ajd.A)= (adj.A)A.

Show that [[1,1],[0,1]]^2 = [[1,3],[0,1]]