If A=`[{:(,3,-4),(,1,-1)]:}` then show that `A^(3)=[{:(,7,-12),(,3,-5)]:}`

if A=[{:(3,1),(-1,2):}], show that A^(2)-5A+7I=0.

If A=|[1,2],[3,2]| ,then show that |2A|=4|A|

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=[{:(3,1),(-1,2):}] , show that A^(2)-5A+7I=O . Hence, find A^(-1) .

if A=[{:(1,0,-3),(2,3,4),(-4,5,-2):}]and b=[{:(3,0,-1),(2,5,-4),(4,-1,2):}], then show that : (AB)'=B'A'

If A=[(5,3),(12,7)] , show that A^(2)-12A-I=0 . Hence find A^(-1) .

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

If A={:[(2,3,5,6),(-1,2,-3,4)]:}andB={:[(4,-5,3,7),(8,-3,-1,2)]:} , then find A^(T)+B^(T)and(A+B)^(T) . What do you notice ?

If A{:[(1,2,3,5,6),(4,-1,2,-3,1)]:}andB={:[(5,3),(2,1),(-3,5),(4,1),(1,2)]:} , then find AB and BA.

If A=[(5,2),(-1,2)] and I=[(1,0),(0,1)] show that : (A-3I)(A-4I)=O