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We show that a matroid M is weakly orientable if and only if the element cM (an abstraction of -1) of its Tutte group is not a square. LINEAR ALGEBRA AND ITS APPLICATIONS 117: 21-24 (1989) 21 0doi:10.1016/0024-3795(89)90544-2 fatcat:xfv4rqp6kbaixewoj5y2srihj4