Read the two statements and choose the correct option.

I. If $|A| \ne 0$, the system $AX = B$ has a unique solution.

II. If $|A| = 0$ and $(\operatorname{adj} A)B = O$, the system $AX = B$ has no solution.

Explanation

1. 01

   With $|A| \ne 0$, $A^{-1}$ exists and $X = A^{-1}B$ is the one solution, so I is true.

2. 02

   With $|A| = 0$ and $(\operatorname{adj} A)B = O$, the system may have infinitely many solutions (as $2x + 3y = 5$, $4x + 6y = 10$ does), so II is false.