That's essentially the definition. φ is the solution to

    φ^2 - φ - 1 = 0

Which can be re-arranged, by dividing by φ to,

    φ - 1 - 1/φ = 0

or:

    1/φ = φ - 1

Or

φ^-1=φ-1

Yes, φ^-1 is another way to write 1/φ.

Yeah but the 【 ａｅｓｔｈｅｔｉｃｓ】

Happy phi day ^_^