  A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper
subsets (called blocks) of a point-set with $v$ points satisfying (i) every two
blocks intersect each other in $\lambda$ points for a fixed $\lambda < v$ (ii)
there are at least two block sizes. A design $\mathcal{D}$ is called a
symmetric design, if all the blocks of $\mathcal{D}$ have the same size
  (or equivalently, every point has the same replication number) and every two
blocks intersect each other in $\lambda$ points. The only known construction of
a Ryser design is via block complementation of a symmetric design also known as
the Ryser-Woodall complementation method. Such a Ryser design is called a Ryser
design of Type-1. The Ryser-Woodall conjecture states: "every Ryser design is
of Type-1".
  Main results of the present article are the following. An expression for the
inverse of the incidence matrix $\mathsf{A}$ of a Ryser design is obtained. A
necessary condition for the design to be of Type-1 is obtained. A well known
conjecture states that, for a Ryser design on \textit{v} points $\mbox{
}4\lambda-1\leq v\leq\lambda^2+\lambda+1$.
  A partial support for this conjecture is obtained. Finally a special case of
Ryser designs with two block sizes is shown to be of Type-1.
