Question 152
Two ordered pairs $(a, b)$ and $(c, d)$, where $a, b, c, d$ are real numbers, form a basis of the coordinate plane if $a d \neq b c$. Determine the number of ordered quadruples $(a, b, c, d)$ of integers between $1$ and $3$ inclusive for which $(a, b)$ and $(c, d)$ form a basis for the coordinate plane.