Why Do Eigenvalues of A+B Equal the Sum of Eigenvalues of A and B?

[tatianaiistb]

Homework Statement

I solved a problem that asked me to show that the sum of the eigenvalues of A+B equals the sum of all the individual eigenvalues of A and B, and similarly for products. I just would like to know why is this so...

Homework Equations

The Attempt at a Solution

Is it because we're combining A and B?

 

[tatianaiistb]

I forgot to mention A and B are 2 by 2 matrices

 

[Mark44]

Homework Statement

I solved a problem that asked me to show that the sum of the eigenvalues of A+B equals the sum of all the individual eigenvalues of A and B, and similarly for products. I just would like to know why is this so...

Since you solved this problem, then you should know why this is so.

Homework Equations

The Attempt at a Solution

Is it because we're combining A and B?