Proving σ([a]) = [5a + 3] is bijective on Z_11

[Danielm]

Homework Statement

Let σ : Z_11 → Z_11 be given by σ([a]) = [5a + 3]). Prove that σ is bijective.

Homework Equations

The Attempt at a Solution

I am just wondering if I can treat σ as a normal function and prove that is bijective by using the definitions of one to one and onto.

 

[Mark44]

Homework Statement

Let σ : Z_11 → Z_11 be given by σ([a]) = [5a + 3]). Prove that σ is bijective.

Homework Equations

The Attempt at a Solution

I am just wondering if I can treat σ as a normal function and prove that is bijective by using the definitions of one to one and onto.

Yes, so long as you keep in mind how σ is defined, as regards what equivalence class maps to what other equivalence class.