(i) $\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0&0\\0&1&0\\0&0&1\end{array}} \right|$
(ii) $\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0&4\\3&5&{ - 1}\\0&1&2\end{array}} \right|$

(i) Let $P = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0&0\\0&1&0\\0&0&1\end{array}} \right|$ ,

we have
${M_{11}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0\\0&1\end{array}} \right| = 1,{M_{12}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0&0\\0&1\end{array}} \right| = 0,{M_{13}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0&1\\0&1\end{array}} \right| = 0$

${M_{21}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0&0\\0&1\end{array}} \right| = 0,{M_{22}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0\\0&1\end{array}} \right| = 1,{M_{23}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0\\0&1\end{array}} \right| = 0$

${M_{31}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0&0\\0&1\end{array}} \right| = 0,{M_{32}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0\\0&1\end{array}} \right| = 0,{M_{33}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&1\\0&1\end{array}} \right| = 1$
For cofactors,

we know that ${P_{ij}} = {( - 1)^{i + j}}{M_{ij}}$

${P_{11}} = 1,{P_{12}} = 0,{P_{13}} = 0,{P_{21}} = 0,{P_{22}} = 1,{P_{23}} = 0,{P_{31}} = 0,{P_{32}} = 0,{P_{33}} = 1$

(ii) Let $P = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0&4\\3&5&{ - 1}\\0&1&2\end{array}} \right|$ ,

we have
${M_{11}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}5&{ - 1}\\1&2\end{array}} \right| = 10 + 1 = 11,{M_{12}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}3&{ - 1}\\0&2\end{array}} \right| = 6,{M_{13}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}3&5\\0&1\end{array}} \right| = 3$

${M_{21}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0&4\\1&2\end{array}} \right| = - 4,{M_{22}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&4\\0&2\end{array}} \right| = 2,{M_{23}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0\\0&1\end{array}} \right| = 1$

${M_{31}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0&4\\5&{ - 1}\end{array}} \right| = - 20,{M_{32}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&4\\3&{ - 1}\end{array}} \right| = - 13$

${M_{33}} = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0\\3&5\end{array}} \right| = 5$

For cofactors,

we know that ${P_{ij}} = {( - 1)^{i + j}}{M_{ij}},$

${P_{11}} = 11,{P_{12}} = - 6,{P_{13}} = 3,{P_{21}} = 4,{P_{22}} = 2,{P_{23}} = - 1,{P_{31}} = - 20,{P_{32}} = 13,{P_{33}} = 5$