Proof by Induction: Showing AnAm = An+m

[annoymage]

Homework Statement

A= (1-n -n

n 1+n)

this is 2x2 matrix, sorry but i don't know which latex to use.


Show that A_nA_m = A_n+m

Homework Equations

n/a

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 A_nA_m = A_n+m

Homework Equations

n/a

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