(a) Prove by induction that (b) Prove by contradiction that \sqrt{21}-\sqrt{10}>\sqrt{2} \left(\begin{array}{cc}

1 & 0 \\

-1 & 1

\end{array}\right)^{n}=\left(\begin{array}{cc}

1 & 0 \\

-n & 1

\end{array}\right), \quad \forall n \geq 0