Is it possible for a homogeneous system with three unknowns and three rows to be inconsistent?

Question

Please provide an explanation. Thank you.

Answer 1

No. Every homogeneous system has, at least, the trivial solution (all unknowns equal to 0).

If the number of equations equals the number of unknowns, then, if the system determinant is 0, the system has only one (the trivial) solution; otherwise, it has ifinitely many solutions.

Answer 2

No.  A system is inconsistent when no solution exists, and every homogeneous system has at least one solution, the trivial one.