Given that,
$\begin{aligned} O(A) &=2 \times 3, O(B)=3 \times 2 \\ O(C) &=3 \times 3 \\ \Rightarrow O\left(A^{\prime}\right) &=3 \times 2, O\left(B^{\prime}\right)=2 \times 3 \\(a) C\left(A+B^{\prime}\right) \end{aligned}$
Now, $O\left(A+B^{\prime}\right)=2 \times 3$
and $O(C)=3 \times 3$
So, matrix $C\left(A+B^{\prime}\right)$ cannot be determined.
(b) $C\left(A+B^{\prime}\right)^{\prime}$
$O\left(A+B^{\prime}\right)=2 \times 3$
$\Rightarrow O\left(A+B^{\prime}\right)^{\prime}=3 \times 2$ and $O(C)=3 \times 3$
Therefore, matrix $C\left(A+B^{\prime}\right)^{\prime}$ can be determined.
(c) $O(B A)=3 \times 3$ and $O(C)=3 \times 3$
Therefore, matrix $B A C$ can be determined.
(d) $C B+A^{\prime}$
Now, order of $C B=($ order of $C$ ) (order of $B$ )
$=($ order of $C$ is $3 \times 3$ ) (order of $B$ is $3 \times 2$ )
$=$ order of $C B$ is $3 \times 2$
Since, $O\left(A^{\prime}\right)=3 \times 2$
Therefore, matrix $C B+A^{\prime}$ can be determined.