4.If `A= [[2,3,1],[-1,2,3],[1,0,2]]`. Prove that `(A')^-1 = (A^-1)'`

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

If A=[[1, 0 ,2 ],[0 ,2 ,1],[2, 0 ,3]] , prove that A^3-6A^2+7A+2I=0

If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

If A =[[1,2,3],[-1,0,2],[1,-3,-1]] , B= [[4,5,6],[-1,0,1],[2,1,2]] and C=[[-1,-2,1], [-1,2,3],[-1,-2,2]] verify that A(B+C)=AB+AC .

Prove that : 1+2+3++n=(n(n+1))/2

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

if A =[{:(1,0,2),(0,2,1),(2,0,3):}] , prove that A^3-6A^2+7A+2I=0

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 .

4) find the rank of [[1,-3,1,2],[0,1,2,3],[3,4,1,-2]]

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