Suppose that $A$ is an $n \times n$ matrix with $n=10$ and $b$ is an $n \times 1$ vector. Suppose that the equation $Ax=b$ for an $n \times 1$ vector does not admit any solution. Which of the following conclusions can be drawn from the given information?
- $A^{-1}$ does not exist
- The equation $A^T x= b$ also does not admit any solution
- $|A|$ = 0
- Suppose $c$ is another $n\times 1$ vector such that $Ax = c$ also does not admit a solution. Then the vector $c$ is a constant multiple of the vector $b$
