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Let \(\mathbf{A}=\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}\) and \(\mathbf{B}=\begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}\).
  1. Calculate the product \(\mathbf{A}\mathbf{B}\).
  2. Based on this result, can you conclude whether \(\mathbf{B}\) is the inverse of \(\mathbf{A}\)?

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