Consider the system Ax=bAx = bAx=b where det(A)=5\det(A) = 5det(A)=5. Is the system solvable for a unique xxx?
Yes, because det(A)≠0\det(A) \neq 0det(A)=0.
No, because det(A)≠1\det(A) \neq 1det(A)=1.
Yes, but only if b=0b=0b=0.
No, it is inconsistent.