Answer
No
Work Step by Step
We are given the matrices:
$A=\begin{bmatrix}0&2&0\\3&3&2\\2&5&1\end{bmatrix}$
$B=\begin{bmatrix}-3.5&-1&2\\0.5&0&0\\4.5&2&-2\end{bmatrix}$
In order to check if $B$ is the multiplicative inverse of $A$, we have to compute $AB$ and $BA$ and see if $AB=BA=I_3$.
Compute $AB$:
$AB=\begin{bmatrix}0&2&0\\3&3&2\\2&5&1\end{bmatrix}\begin{bmatrix}-3.5&-1&2\\0.5&0&0\\4.5&2&-2\end{bmatrix}$
$=\begin{bmatrix}0+1+0&0+0+0&0+0+0\\-10.5+1.5+9&-3+0+4&6+0-4\\-7+2.5+4.5&-2+0+2&4+0-2\end{bmatrix}$
$=\begin{bmatrix}1&0&0\\0&1&2\\0&0&2\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\not=I_3$
Compute $BA$:
$BA=\begin{bmatrix}-3.5&-1&2\\0.5&0&0\\4.5&2&-2\end{bmatrix}\begin{bmatrix}0&2&0\\3&3&2\\2&5&1\end{bmatrix}$
$=\begin{bmatrix}0-3+4&-7-3+10&0-2+2\\0+0+0&1+0+0&0+0+0\\0+6-4&9+6-10&0+4-2\end{bmatrix}$
$=\begin{bmatrix}1&0&0\\0&1&0\\2&5&2\end{bmatrix}\not=I_3$
As $AB\not=BA$, $B$ is not the multiplicative inverse of $A$.
