The number of 3x3 matrices A whose entries are either 0 or 1 and for which the system Axyz = 100 has exactly two distinct solutions, is:

Given Axyz = 100
The system of equation has three equations in three unknowns. Each equation represents a plane in three-dimensional space. We know that no three planes can intersect at only two distinct points. So, the system cannot have exactly 2 distinct solutions. It can have a unique or no solution or infinitely many solutions. Hence, there is no such matrix A.