The LUApply function applies the permutation pvec and the forward and backward substitutions encoded in A directly to the right-hand side mod m Matrix or Vector B, where pvec and A are the output of the LUDecomposition function.

B must have the same number of rows as columns in A.

The function works directly on B, returning the solution in B on successful completion. If the function fails, B can be altered.

LUApply is simply the application of Permute, ForwardSubstitute, and then BackwardSubstitute.

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form LUApply(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][LUApply](..).