Strong linear preservers of rank reverse permutability on triangular matrices

Let F be a field with ∣F∣ > 2 and Tn(F) be the set of all n × n upper triangular matrices, where n ⩾ 2. Let k ⩾ 2 be a given integer. A k-tuple of matrices A1, …, Ak ∈ Tn(F) is called rank reverse permutable if rank(A1A2 ⋯ Ak) = rank(AkAk−1 ⋯ A1). We characterize the linear maps on Tn(F) that strongly preserve the set of rank reverse permutable matrix k-tuples.