using LinearAlgebra
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σ = [1, 4, 2, 5, 3] # 1->1, 2->4, 3->2, 4->5, 5->3
v = [6, 7, 8, 9, 10]
5-element Vector{Int64}:
P = I(5)[σ,:]
5-element Vector{Int64}:
inv(Matrix(P)) == P’
σ⁻¹ = [1,3,5,2,4]
P⁻¹ = I(5)[σ⁻¹,:]
P⁻¹ == P’ == inv(Matrix(P))
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