What happens to the eigenvalues when a constant is multiplied to a matrix?

[Cosmossos]

Hello,
Let's say I have a 2x2 matrix,we call it A with the eigenvalues +1 , -1.
Now I let's define that m=m0*A. (m0 is const).
Are the eigenvalues become +m0 and -m0?
If so why?

 

[elibj123]

Because if $$\lambda$$ satisfies $$det(A-\lambda I)=0$$ then $$\lambda'=m_{0}\lambda$$ satisfies $$det(M-\lambda' I)=0$$, with $$M=\lambda' A$$
You simply multiply the equation by $$m^{2}_{0}$$ (and under the determinant it becomes just $$m_{0}$$)/
Therefore $$m_{0}\lambda$$ are eigenvalues of $$m_{0}A$$.