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#### a)

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\$\\begin{eqnarray*} AB &=& \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\simplify[]{{a11}{b11}+{a12}{b21}}&\\simplify[]{{a11}{b12}+{a12}{b22}}\\\\ \\simplify[]{{a21}{b11}+{a22}{b21}}&\\simplify[]{{a21}{b12}+{a22}{b22}}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\var{ab11}&\\var{ab12}\\\\ \\var{ab21}&\\var{ab22}\\\\ \\end{pmatrix} \\end{eqnarray*} \$

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#### b)

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\$\\begin{eqnarray*} CB &=& \\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\simplify[]{{c11}{b11}+{c12}{b21}}&\\simplify[]{{c11}{b12}+{c12}{b22}}\\\\ \\simplify[]{{c21}{b11}+{c22}{b21}}&\\simplify[]{{c21}{b12}+{a22}{b22}}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\var{cb11}&\\var{cb12}\\\\ \\var{cb21}&\\var{cb22}\\\\ \\end{pmatrix} \\end{eqnarray*} \$

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More information on multiplying matrices can be found in the 'Matrices' section on our Maths Study Skills page.

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", "name": " Matrix Multiplication (2x2)", "metadata": {"description": "

Multiplication of $2 \\times 2$ matrices.

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$AB = \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix} =$ [[0]]

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$CB = \\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix} \\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}=$ [[0]]

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Let
\$A=\\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix},\\;\\; B=\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix},\\;\\; C=\\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}\$
Calculate the following products of these matrices:

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