Is the null matrix a regular matrix?

Question

I see there are different qualities of a regular matrix depending on definition. Is the null matrix (nxn) regular in any of them ?

Answer 1

A regular matrix is nonsingular (has an inverse). The zero matrix is not invertible. So, no, the zero matrix is not regular.

Answer 2

All definitions of a regular matrix are equivalent, so no, the zero matrix will never be regular.