We apply the method of determinants to study the distribution of the largest
singular values of large $ m \times n $ real rectangular random matrices with independent
Cauchy entries. We show that statistical properties of the (rescaled by a factor of $
\frac{1}{m^2\*n^2}$)largest singular values agree in the limit with the statistics of the
inhomogeneous Poisson random point process with the intensity $ \frac{1}{\pi} x^{-3/2} $
and, therefore, are different from the Tracy-Widom law. Among other corollaries of our
method we show an interesting connection between the mathematical expectations of the
determinants of complex rectangular $ m \times n $ standard Wishart ensemble and real
rectangular $ 2m \times 2n $ standard Wishart ensemble.