Answer
$a.\qquad $BC is not defined
$b.\qquad BF=\left[\begin{array}{rrr}
3 & 1/2 & 5\\
1 & -1 & 3
\end{array}\right]$
Work Step by Step
If $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix
(so the number of columns of $A$ is the same as the number of rows of $B$),
then the matrix product $AB$ is the $m\times k$ matrix
whose $ij$-entry is the inner product of the $i\mathrm{t}\mathrm{h}$ row of $A$ and the jth column of $B.$
---
$a.$
$B$ is a 2$\times$3 matrix. C does not have 3 rows.
BC is not defined
$b.$
$BF$ is defined and is a 2$\times$3 matrix
$BF=\left[\begin{array}{lll}
3+0+0 & 0+1/2+0 & 0+0+5\\
1+0+0 & 0+(-1)+0 & 0+0+3
\end{array}\right]$
$=\left[\begin{array}{lll}
3 & 1/2 & 5\\
1 & -1 & 3
\end{array}\right]$
