Which of the following statements is/are correct?

\([1]\) An irrational number times a rational number is always an irrational number.

\([2]\) The statement \(\tan^{-1} x + \tan^{-1} y=\tan^{-1}\left( \frac{x+y}{1-xy}\right)\) is true for all real numbers \(x\) and \(y\).

\([3]\) If \(x^y=y^x\), then \(x=y\) where \(x\) and \(y\) are positive real numbers.

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