  By using the matrix-model representation, we show that correlation numbers of
boundary changing operators (BCO) in $(2,2p+1)$ minimal Liouville gravity
satisfy some identities, which we call the null identities. These identities
enable us to express the correlation numbers of BCO in terms of those of
boundary preserving operators. We also discuss a physical implication of the
null identities as the manifestation of the boundary interaction.
