julia> using SparseArrays, Random

julia> A = sprand(10^6, 10^6, 10 / (10^6))

julia> a = randperm(size(A,1))

julia> @time A[a, a];
  1.871472 seconds (3.00 M allocations: 373.896 MiB, 10.60% gc time)

julia> @time A[a, a];
  1.414649 seconds (31 allocations: 206.057 MiB, 6.81% gc time)