Operator Square

Let the operator \(\square\) be defined for all positive integers the following way:

  • \(1 \square 1=1\).
  • For all positive integers \(n>1\), \(n \square 1=(n-1) \square 1+n\).
  • For all positive integers \(n>1\), \(1 \square {n}=1 \square (n-1)+n\).
  • For all positive integers \(a>1\) and \(b>1\), \(a\square{b}=a\square(b-1)+(a-1)\square{b}\).

Evaluate \(5\square5\).

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