"multiplying by itself until all entries are positive"?? Who told you this way you can find out whether a matrix is regular? Take, for example, the real 2x2 matrix whose all entries are 1: all its elements are positive but it is not regular.
A nice way is calculating its determinant: the matrix is regular iff its the determinant is non zero.
Another way: bring your matrix to echelon form though elementary operations on its rows (or columns): then the matrix is regular iff at no step a row (or column) becomes all zeroes.
There are severaa other characterizations of regular matrices but the above two are, perhaps, of the more basic ones.