$A$ is an $n\times n$ matrix.

Check the true statements below:

A. An eigenspace of $A$ is just a null space of a certain matrix.
B. A steady-state vector for a stochastic matrix is actually an eigenvector.
C. If $v_{1}$ and $v_{2}$ are linearly independent eigenvectors, then they correspond to distinct eigenvalues.
D. If $Ax = \lambda x$ for some vector $x$, then $x$ is an eigenvector of $A$.
E. The eigenvalues of a matrix are on its main diagonal.