Question

Find the inverse of each of the matrices (if it exists). $\begin{bmatrix}1&0&0\\\3&3&0\\\5&2&-1\end{bmatrix}$

Answer 1

Let A=$\begin{bmatrix}1&0&0\\\3&3&0\\\5&2&-1\end{bmatrix}$

we have IAI=1(-3-0)-0+0=-3
now A11=-3-0=-3, A12=-(-3-0)=3, A13=6-15=9
A21=-(0-0)=0, A22=-1-0=-1,A23=-(2-0)=-2
A31=0-0=0,A32=-(0-0)=0,A33=3-0=3

therefore adj A=$\begin{bmatrix}-3&0&0\\\3&-1&0\\\\-9&-2&3\end{bmatrix}$

so A-1=$\frac{1}{\mid A \mid}$adj A=-\frac{1}{3}$$\begin{bmatrix}-3&0&0\\\3&-1&0\\\\-9&-2&3\end{bmatrix}