Which one of the following options is incorrect?

For a square matrix A in the matrix equation AX = B.

If $|A| \neq 0$ and $(adj A) B \neq 0$ then there is no solution

for AX = B

1 → |A| $\neq 0 \Rightarrow$ unique soln → correct

2 →|A| = 0 (Adj } A) B \neq 0 \Rightarrow$ no solution → correct 

3 → |A| $neq 0$ (Adj A) B $\neq 0 \Rightarrow$ no solution → incorrect

4 → |A| = 0 $\Rightarrow$ (adj A)B = 0 $\Rightarrow$  infinite soln → correct