MATL, 9 bytes
Z^t!dXAY)
Explanation
Z^ % Implicit inputs. Cartesian product. EachGives Cartesiana tuplecharacter matrix where
% each row is a rowCartesian tuple (*)
t! % Duplicate, transpose
d % Consecutive differences, computed along vertical dimension
XA % Vertical-all: gives true for columns that only contain nonzeros
Y) % Use as logical index into the rows of (*). ImpliciyImplicit display