Prove that n*P( n -1,n - 1) = P (n, n)

$P(n,k) = {\frac{n!} {(n-k)!}}$

$P(n,n) = {\frac {n!} {(n-n)!}} = n!$

The point is to prove that $n*P(n-1,n-1) = n!$

$n*P(n-1,n-1) = n*{\frac {(n-1)!} {((n-1)-(n-1))!}}=n*(n-1)!=n!$

The statement has been proven