If `A=[1 0 1 0 1 2 0 0 4]` , then show that `|3A|" "=" "27|A|`

if A = [[-1, 1 ],[0 ,4 ]] and B = [ [ -3 , 2 ] , [ 0 ,-1 ] ] then show that ( A + B )^2

If A=|[1,0,1],[0,1,2],[0,0,4]| then |3A|

If (a + 1/a )^2 = 3 and a ne 0 , then show that a^3 + 1/a^3 = 0

If (a + 1/a )^2 = 3 and a ne 0 , then show that a^3 + 1/a^3 = 0

If A=[[0,0,1],[0,1,0],[1,0,0]] , show that A^(-1)=A

If A=[(1,0),(0,3)] and B=[(2,0),(0,1)] then show AB =BA =[(2,0),(0,3)]

If A=[(3,-3,4),(2,-3,4),(0,-1,1)]2-3 41 then show that A^-1=A^1.

If A=[[1,0],[0,1]],B=[[1,0],[0,-1]] and C=[[0,1],[1,0]] then show that A^(2)=B^(2)=C^(2)

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

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.