Finding Number of Nonzero eigenvalues

Question

$A$ is a $3\times3$ non-zero matrix such that $A^2=0$. To find number of non-zero eigenvalues of $A$. How to approach? If you can suggest a good easy to understand study material that would be really helpful.

Answer 1

Well after searching here and there I have a conclusion that A has no Nonzero eigenvalues.

AX=CX => (A^2)X=(C^2)X

Now A^2=0, So C^2=0, i.e. C=0

Can anyone confirm?