If `3A=[[1,2,2],[2,1,-2],[-2,2,-1]]`then show that `A^(-1)=A^(T)`

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

.If A=[[1,4,7],[2,5,8]] and B=[[-3,4,0],[4,-2,-1]] then show that (A+B)^T=A^T+B^T

If A=[(-1,-2,-2 ),(2, 1,-2),( 2,-2 ,1)] , show that a d j\ A=3A^T .

if A=[{:(1,-1,1),(2,1,-1),(-1,-2,2):}] then show that A^(-1) Does not exist.

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

Find the adjoint of the matrix A=[(-1,-2,-2), (2 ,1,-2), (2,-2, 1)] and hence show that A(a d j\ A)=|A|\ I_3 .

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

If A=[{:(,1,1,2),(,0,2,1),(,1,0,2):}] show that A^(3)=(5A-I)(A-I)

If A+I={:[(2,2,3),(3,-1,1),(4,2,2)]:} then show that A^(3)-23A-40I=0

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