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

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

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

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

(i) if A=[{:(4,-1,-4),(3,0,-4),(3,-1,-3):}], then show that A^(2)=I

If A=[(1,-2,3),(4,5,-1),(5,0,2)] find 3A

if A[{:(1,3,-1),(2,2,-1),(3,0,-1):}]and B=[{:(-2,3,-1),(-1,2,-1),(-6,9,-4):}], then show that AB=BA.

if A[{:(2,-3,-5),(-1,4,5),(1,-3,-4):}]and B=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}], then show that (i) AB=A and BA=B.

if A=[{:(2,1,3),(1,-1,2),(4,1,5):}]and B=[{:(1,-1,2),(2,1,5),(4,1,3):}], then show that : (i) (A+B)'=A'+B' (ii) (A+4B)'=A'+4B'

If A=[1 2 3 3-2 1 4 2 1] , then show that A^3-23 A-401=0 .