Retaining the property of Symmetric?

General Usage
, , ,
4

The current behavior is

julia> S
3×3 Symmetric{Int64, Matrix{Int64}}:
  0  -8  -2
 -8  -2   3
 -2   3   8

julia> S^2
3×3 Symmetric{Int64, Matrix{Int64}}:
  68  10  -40
  10  77   34
 -40  34   77

julia> S * S
3×3 Matrix{Int64}:
  68  10  -40
  10  77   34
 -40  34   77

julia> transpose(S) * S
3×3 Matrix{Int64}:
  68  10  -40
  10  77   34
 -40  34   77

julia> S .^ 2
3×3 Matrix{Int64}:
  0  64   4
 64   4   9
  4   9  64