ASL structures of some quadrics

Let K be a field and X, Y denote matrices such that, the entries of X are either indeterminates over K or 0 and the entries of Y are indeterminates over K which are different from those appearing in X. We consider ideals of the form I1(XY), which is the ideal generated by the 1?1 minors of the matrix XY. We prove that the quotient ring K[X,Y]/I1(XY) admits an ASL structure for certain X and Y.