Eigen Values and Rank?

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Can anyone plz tell me wheher 0 is eigen value or not?

Secondaly if i have solved the matrix for eigen values and i got two vlaues i.e. 3 and 0 at the end than will rank be alwz 1 for that matrix?

waiting.....
 

Hi
0 is an eigenvalue if the matrix is rank deficient, because then there exist solution x ≠ 0 for

Ax = 0

so the eigenvalue equation Ax = λx has a solution for x when λ = 0
If m is the size of the matrix and n its rank, the matrix will have m-n eigenvalues 0.
 

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