Verified answer

[tex]\Large\displaystyle\text{$\begin{gathered} \sf{\begin{array}{|c c c|} \sf-2&\sf1&\sf3\\\sf4&\sf-3&\sf1\\\sf2&\sf4&\sf1 \end{array} } \begin{array}{c c |} \sf-2&\sf1\\\sf4&\sf-3\\\sf2&\sf4 \end{array}\end{gathered}$}[/tex]

[tex]\Large\displaystyle\text{$\begin{gathered} \sf{det=(-2\cdot(-3)\cdot1+1\cdot1\cdot2+3\cdot4\cdot4)-\\\sf(1\cdot4\cdot1+(-2)\cdot1\cdot4+3\cdot(-3)\cdot2) } \end{gathered}$}[/tex]

[tex]\Large\displaystyle\text{$\begin{gathered} \sf{det=(6+2+48) -(4-8-18)} \end{gathered}$}[/tex]

[tex]\Large\displaystyle\text{$\begin{gathered} \sf{det=56-(-22) } \end{gathered}$}[/tex]

[tex]\Large\displaystyle\text{$\begin{gathered} \sf{ det=56+22} \end{gathered}$}[/tex]

[tex]\Large\displaystyle\text{$\begin{gathered} \boxed{\boxed{\sf{det=78 }}} \end{gathered}$}[/tex]

| -2 1 3 | -2 1

| 4 -3 1 | 4 -3

| 2 4 1 | 2 4

det=(-2*(-3)*1+1*1*2+3*4*4)-(1*4*1+(-2)*1*4+3*(-3)*2)

det= (6+2+48)-(4-8-18)

det=56-(4-8-18)

det=56-(-22)

det=56+22

det=78