Suppose zero is an eigenvalue of the matrix A what does that

Suppose zero is an eigenvalue of the matrix A. what does that tell you about the multispecies of A? Is A invertible or not?

Solution

There must be some nontrivial
vector x for which
Ax = 0x = 0
which implies that A is not invertible which implies a whole lot of things given our Invertible Matrix
Theorem.
Invertible Matrix Theorem: The n × n matrix A is invertible if and only if 0 is not an
eigenvalue of A