$\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&{ - 1}&2\\2&3&5\\{ - 2}&0&1\end{array}} \right]$

Let $P = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&{ - 1}&2\\2&3&5\\{ - 2}&0&1\end{array}} \right].$ Let ${A_{ij}}$

be cofactors of ${a_{ij}}$ in A.

Then,
${A_{11}} = {( - 1)^{1 + 1}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}3&5\\0&1\end{array}} \right] = 3 - 0 = 3$

${A_{12}} = {( - 1)^{1 + 2}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&5\\{ - 2}&1\end{array}} \right] = - (2 + 10) = - 12$

${A_{13}} = {( - 1)^{1 + 3}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&3\\{ - 2}&0\end{array}} \right] = 0 + 6 = 6$

${A_{21}} = {( - 1)^{2 + 1}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{ - 1}&2\\0&1\end{array}} \right] = - ( - 1 - 0) = 1$

${A_{22}} = {( - 1)^{2 + 2}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2\\{ - 2}&1\end{array}} \right] = 1 + 4 = 5$

${A_{23}} = {( - 1)^{2 + 3}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&{ - 1}\\{ - 2}&0\end{array}} \right] = - (0 - 2) = 2$

${A_{31}} = {( - 1)^{3 + 1}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{ - 1}&2\\3&5\end{array}} \right] = - 5 - 6 = - 11$

${A_{32}} = {( - 1)^{3 + 2}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2\\2&5\end{array}} \right] = - (5 - 4) = - 1$

${A_{33}} = {( - 1)^{3 + 3}}\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&{ - 1}\\2&3\end{array}} \right] = 3 + 2 = 5$

% $\therefore$ $adj$ $P = {\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}3&{ - 12}&6\\1&5&2\\{ - 11}&{ - 1}&5\end{array}} \right]^{\prime}} = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}3&1&{ - 11}\\{ - 12}&5&{ - 1}\\6&2&5\end{array}} \right]$