There are multiple results which finish this problem immediately, so it depends what you know. Probably the easiest method is to note that if denotes the multiset of eigenvalues (i.e. all the eigevalues, including multiples) then . Thus, if is singular then from where it follows that is in whatever the underlying field you're working with (if that last part didn't make sense replace it with "since the s are in ) it follows that at least one element of must be zero.

Anothe direction is that is singular if and only if for some , but I doubt you know what since this is, basically the question.