1950 AHSME Problem 38

If the expression \begin{pmatrix}a & c\\ d & b\end{pmatrix} has the value ab-cd for all values of a, b, c and d, then the equation \begin{pmatrix}2x & 1\\ x & x\end{pmatrix}= 3:

\begin{array}{l} \textbf{(A)}\ \text{Is satisfied for only 1 value of }x\qquad\\ \textbf{(B)}\ \text{Is satisified for only 2 values of }x\qquad\\ \textbf{(C)}\ \text{Is satisified for no values of }x\qquad\\ \textbf{(D)}\ \text{Is satisfied for an infinite number of values of }x\qquad\\ \textbf{(E)}\ \text{None of these.} \end{array}

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