1. The problem asks for the maximum possible number of leading 1's in the reduced row echelon form (RREF) of a matrix $A$ that is $5 \times 3$ (5 rows and 3 columns). 2. The leading 1's in RREF correspond to the pivots or the rank of the matrix. 3. The rank of a matrix cannot exceed the smaller of the number of rows or columns. 4. Since $A$ has 5 rows and 3 columns, the maximum rank is $\min(5,3) = 3$. 5. Therefore, the maximum number of leading 1's in the RREF of $A$ is 3. 6. Among the options given, the correct answer is A. 3.