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      <text>8.2.1.2 Example determinant and inverse matrix</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<p>Given the matrix <span class="math display">\[A=\left[\begin{array}{rr}2&amp;3\\ 1&amp;-2\end{array}\right]\]</span> find its determinant. What does this tell you about <span class="math inline">\(A^{-1}\)</span>?</p>
<h4 class="HELM_solution">Solution</h4>
<p><span class="math display">\[|A|=2\times (-2)-1\times 3=-7.\]</span> Since <span class="math inline">\(|A|\neq 0\)</span> then <span class="math inline">\(A^{-1}\)</span> exists. Therefore, we can now find <span class="math inline">\(A^{-1}\):</span></p>

<p><span class="math display">\[A^{-1}=\dfrac{1}{(-7)}\left[\begin{array}{rr}-2&amp;-3\\
-1&amp;2\end{array}\right]=\dfrac{1}{7}\left[\begin{array}{rr}2&amp;3\\ 1&amp;-2\end{array}\right]\]</span></p>]]></text>
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