proof by induction

[annoymage]

1. The problem statement, all variables and given/known data

A= (1-n -n

n 1+n)

this is 2x2 matrix, sorry but i dont know which latex to use.


Show that AnAm = An+m
2. Relevant equations

n/a

3. The attempt at a solution

how do you proof by induction when there's 2 variable?

[annoymage]

1-n , -n



n , 1+n

[willem2]

Show that AnAm = An+m
2. Relevant equations

n/a

3. The attempt at a solution

how do you proof by induction when there's 2 variable?

You do induction on one of the variables and leave the other with universal
quantifier

You take as base case: For all n A_n A_0 = A_{0+n}

and the induction hypthesis: For all n A_n A_m = A_{m+n}

and try to prove For all n A_n A_{m+1} = A_{m+1+n}

[annoymage]

oooo, i see i see,
thank you very much. :)

[willem2]

It's actually easier to just compute the product of A_m and A_n

[annoymage]

yeaaa, it is, why didn't i think of that. =.=

hoho thanks again