prove that n.P(n-1,n-1)=p(n,n)

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$LHS=n.P(n-1,n-1) \\=n\times \dfrac{(n-1)!}{\{(n-1)-(n-1)\}!} \\=n\times \dfrac{(n-1)!}{0!} \\=n(n-1)! \\=n! \\=\dfrac{n!}{0!} \\=\dfrac{n!}{(n-n)!} \\=P(n,n) \\=RHS$

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