Let M be the intersection matrix * . Columns j1 and j2 are said to hook if, for some i, mij1 > 0 and

Let M be the intersection matrix ϒ* ∩ ϒ. Columns j1 and j2 are said to hook if, for some i, mij1 > 0 and mij2 > 0. The set of columns is said to communicate if there exists a sequence j1, j2,…, jν

such that columns j

ι and j

ι+1 hook. The matrix M is said to be indecomposable if its columns communicate. Show that M is indecomposable if and only if MT is indecomposable.