2024 AMC 12A Problem 25

A graph is \textit{symmetric} about a line if the graph remains unchanged after reflection in that line. For how many quadruples of integers (a,b,c,d), where |a|,|b|,|c|,|d|\le5 and c and d are not both 0, is the graph of y=\frac{ax+b}{cx+d}symmetric about the line y=x?

\textbf{(A) }1282\qquad\textbf{(B) }1292\qquad\textbf{(C) }1310\qquad\textbf{(D) }1320\qquad\textbf{(E) }1330

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.