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Write minors and cofactors of the element of $$\left| {\begin{array}{*{20}{c}} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}} \right|$$
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## QuestionMathsClass 12

Write minors and cofactors of the element of $$\left| {\begin{array}{*{20}{c}} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}} \right|$$

Let $$\Delta = \left| {\begin{array}{*{20}{c}} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}} \right|$$
M11 = Minor of $${a_{11}} = \left| {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right| = 1 - 0 = 1$$ and $${A_{11}} = {\left( { - 1} \right)^{1 + 1}}{M_{11}} = {\left( { - 1} \right)^2}\left( 1 \right) = 1$$
M12 = Minor of $${a_{12}} = \left| {\begin{array}{*{20}{c}} 0&0 \\ 0&1 \end{array}} \right| = 0 - 0 = 0$$ and $${A_{12}} = {\left( { - 1} \right)^{1 + 2}}{M_{12}} = {\left( { - 1} \right)^3}\left( 0 \right) = 0$$
M13 = Minor of $${a_{13}} = \left| {\begin{array}{*{20}{c}} 0&1 \\ 0&0 \end{array}} \right| = 0 - 0 = 0$$ and $${A_{13}} = {\left( { - 1} \right)^{1 + 3}}{M_{13}} = {\left( { - 1} \right)^4}\left( 0 \right) = 0$$
M21 = Minor of $${a_{21}} = \left| {\begin{array}{*{20}{c}} 0&0 \\ 0&1 \end{array}} \right| = 0 - 0 = 0$$ and $${A_{21}} = {\left( { - 1} \right)^{2 + 1}}{M_{21}} = {\left( { - 1} \right)^3}\left( 0 \right) = 0$$
M22 = Minor of $${a_{22}} = \left| {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right| = 1 - 0 = 1$$ and $${A_{22}} = {\left( { - 1} \right)^{2 + 3}}{M_{22}} = {\left( { - 1} \right)^4}\left( 1 \right) = 1$$
M23 = Minor of $${a_{23}} = \left| {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right| = 0 - 0 = 0$$ and $${A_{23}} = {\left( { - 1} \right)^{2 + 3}}{M_{23}} = {\left( { - 1} \right)^5}\left( 0 \right) = 0$$
M31 = Minor of $${a_{31}} = \left| {\begin{array}{*{20}{c}} 0&0 \\ 1&0 \end{array}} \right| = 0 - 0 = 0$$ and $${A_{31}} = {\left( { - 1} \right)^{3 + 1}}{M_{31}} = {\left( { - 1} \right)^4}\left( 0 \right) = 0$$
M32 = Minor of $${a_{32}} = \left| {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right| = 0 - 0 = 0$$ and $${A_{32}} = {\left( { - 1} \right)^{3 + 2}}{M_{32}} = {\left( { - 1} \right)^5}\left( 0 \right) = 0$$
M33 = Minor of $${a_{33}} = \left| {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right| = 1 - 0 = 1$$ and $${A_{33}} = {\left( { - 1} \right)^{3 + 3}}{M_{33}} = {\left( { - 1} \right)^6}\left( 1 \right) = 1$$
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