The matrix model for IIB superstring proposed by Ishibashi, Kawai, Kit
azawa and Tsuchiya is investigated. Consideration of planar and non-pl
anar diagrams suggests that large-iii perturbative expansion is consis
tent with the double scaling limit proposed by the above authors. We w
rite down a Wilson loop that can be interpreted as a fundamental strin
g vertex operator. The one-point tadpole in the presence of a D-string
has the right form and this can be viewed as a matrix model derivatio
n of the boundary conditions that define a D-string. We also argue tha
t if worldsheet coordinates sigma and tau are introduced to the fundam
ental string, then the conjugate variable d/d sigma and d/d tau can be
interpreted as the D-string worldsheet coordinates. In this way the S
L(2Z) duality group of the IIB superstring becomes identified with the
symplectic group acting on (p,q).