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Let Mm,n(B) be the semimodule of all m×n Boolean matrices where B is the Boolean algebra with two elements. Let k be a positive integer such that 2⩽k⩽minm,n. Let Bm,n,k denote the subsemimodule of Mm,n(B) spanned by the set of all rank k matrices. We show that if T is a bijective linear mapping on Bm,n,k, then there exist permutation matrices P and Q such that TA=PAQ for all A∈Bm,n,k or m=n and TA=PAtQ...
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