The product, $\log_a b \cdot \log_b a$ is equal to: 
$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ a \qquad \textbf{(C)}\ b \qquad \textbf{(D)}\ ab \qquad \textbf{(E)}\ \text{none of these}$
\[a^x=b\]
\[b^y=a\]
\[{a^x}^y=a\]
\[xy=1\]
\[\log_a b\log_b a=1\]
As a result, the answer should be $\boxed{\textbf{(A) }1}$.