In this article we apply formal matrices technique to get a equivalent proposition of Li Shanian identity, and hence give an elementary proof for Li Shanlan identity.
本文应用形式矩阵的计算技巧，得到李善兰恒等式的一个等价命题，进而给出李善兰恒等式的一个初等证明。
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We generalize the rank of matrices over a division ring to the B-rank of matrices over a ring with identity and study properties for the B-rank of matrices over a ring with identity.