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  <question type="description">
    <name>
      <text>7.2.6.3 Algebra of matrices</text>
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    <questiontext format="moodle_auto_format">
      <text><![CDATA[<p>We now list some properties of matrix multiplication and compare them with corresponding
properties for multiplication of numbers.</p>
<div class="HELM_keypoint">
<h4>Key Point</h4>
\(
\begin{array}{ccc}
\textbf{Matrix algebra} && \textbf{Number algebra} \\
A(B+C) = AB+AC && a(b+c)=ab+ac \\
AB\neq BA\text{ in general} && ab=ba \\
A(BC)=(AB)C && a(bc)=(ab)c \\
AI = IA = A && 1\cdot a=a\cdot1=a \\
A\underline{0} = \underline{0}A=\underline{0} && 0\cdot a=a\cdot0=0 \\
AB\text{ may not be defined} && ab\text{ is always defined} \\
AB=\underline{0}\text{ does not imply }A=\underline{0}\text{ or }B=\underline{0} && ab=0\text{ implies }a=0\text{ or }b=0
\end{array}
\)
</div>]]></text>
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