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.