If \( \mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], \mathrm{B}=\left[\begi...

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If \( \mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right] \) and \( \mathrm{AB}=\mathrm{BA} \), then show that \( \mathrm{B} \) is a scalar matrix.
Hint.
Show that \( a=b \).
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