Presumably, it should be in this link:
If two vectors have the same direction but possibly different lengths the each is a numerical multiple of the other. If M "changes the magniude but not the direction" of m, then Mv= av where a is a number, then applying the linear transformation to this v is just like multiplying by a number, which is much easier.The rules for using a matrix to transform a vector are given in the article linear algebra.
If the action of a matrix on a (nonzero) vector changes its magnitude but not its direction, then the vector is called an eigenvector of that matrix.
Of course, it is true that M0= 0= a0 but if Mv= av for v non-zero, then we say that "a" is an "eigenvalue" of M and v is a corresponding "eigenvector"
It's hard to say more without knowing what you do know and understand about vectors, matrices, linear transformations, and vector spaces.