This question is in matrices.

A^n = [ 1 3^n-1 ; 0 3^n ] for all integers n>=1 where A = [ 1 2 ; 0 3 ]

I got the base step

(B) let P(1) equal A^n = [ 1 3^n-1 ; 0 3^n ].

A^1 = [ 1 3^1-1 ; 0 3^1 ] gives A^1 = [ 1 2 ; 0 3 ] which is the same as the given matrix A^1. Thus P(1) is true.

(R) inductive step

Assume P(n) is true for some (n) E A.

I figured that A^(n+1) = [ 1 3^(n+1)-1 ; 0 3^(n+1) ].

However this is the part that i got stuck because i've never actually done any questions regarding matrices with mathematical induction so im lost.

Could someone help me on this question? or even just give me the starting line for it.