Find the determminant?

I expanded across the first row.

$\displaystyle \begin{vmatrix} 0 & 1 & -2\\ -2 & 2 & 0\\ -3 & 4 & 1 \end{vmatrix}\Rightarrow 0*\begin{vmatrix} 2 & 0 \\ 4 & 1 \end{vmatrix}-1*\begin{vmatrix} -2 & 0 \\ -3 & 1 \end{vmatrix}-2*\begin{vmatrix} -2 & 2 \\ -3 & 4 \end{vmatrix}=0-1*(-2-0)-2*(-8-(-6))=0+2+4=6$

You should be able to do this one by using 1 and 3 as an outline.

$\displaystyle A^{-1}=\frac{1}{det(A)}*A$

$\displaystyle\begin{vmatrix} -4 & 3 \\ 5 & 0 \end{vmatrix}=-4*0-5*3=0-15=-15$

Definition:
The determinant of an n x n matrix A is defined as

$\displaystyle det(A) = \begin{cases} a_{11}, & \mbox{if } \ n=1 \\ a_{11}A_{11}+a_{12}A_{12}+\dots +a_{1n}A_{1n}, & \mbox{if } \ n>1 \end{cases} $

where

$\displaystyle A_{1j}=(-1)^{1+j}det(M_{1j}) \ j=1,2,\cdots , n$

are the cofactors associated with the first row expansion.