AHSME 1950 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 $\begin{pmatrix}2x & 1\\ x & x\end{pmatrix}= 3$: $\textbf{(A)}\ \text{Is satisfied for only 1 value of }x \\ \textbf{(B)}\ \text{Is satisified for only 2 values of }x \\ \textbf{(C)}\ \text{Is satisified for no values of }x \\ \textbf{(D)}\ \text{Is satisfied for an infinite number of values of }x \\ \textbf{(E)}\ \text{None of these.}$