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In a recent work of Ayaka Shimizu$^{[5]}$, she defined an operation namedregion crossing change on link diagrams, and showed that region crossing changeis an unknotting operation for knot diagrams. In this paper, we prove thatregion crossing change on a 2-component link diagram is an unknotting operationif and only if the linking number of the diagram is even.  Besides, we define an incidence matrix of a link diagram via its signedplanar graph and its dual graph. By studying the relation between regioncrossing change and incidence matrix, we prove that a signed planar graphrepresents an $n$-component link diagram if and only if the rank of theassociated incidence matrix equals to $c-n+1$, here $c$ denotes the size of thegraph.

On region crossing change and incidence matrix