Part 1
Now Bob should follow the following steps to decrypt the message
1) First he should arrange the input vector in the form of a 3X3 matrix i.e the first 3 elements form the first column, the next three elements form the second column and so on.
Thus he would get
A= $ \left[ \begin{matrix}1 & 0 & 4 \\ 0 & 1 & 0 \\ 1 & 0 & 1\end{matrix} \right] $
2) Now he should multiply the inverse of the "special matrix" $ M^{-} $ to each column of matrix A to get the respective 3x1 matrices and then combine all three 3x1 matrices to form a new 3x3 matrix
3) Now all he needs to do is replace all the numbers in with their corresponding alphabets and arrange the matrix in the form of a vector.
Eureka!
Part 2
No I don think Eve can decrypt the message without finding out the inverse of the matrix
Part 3
Now the decrypted message is
$ \left[ \begin{matrix}2 \\ 23 \\ 3\end{matrix} \right] $ x $ M^{-} $
$ M^{-} $ = $ \left[ \begin{matrix}1/2 & 0 & 2 \\ 0 & 1 & 0 \\ 1/3 & 0 & 1/3\end{matrix} \right] $
Thus
$ \left[ \begin{matrix}2 \\ 23 \\ 3\end{matrix} \right] $$ M^{-} $ = $ \left[ \begin{matrix}1/2 & 0 & 2 \\ 0 & 1 & 0 \\ 1/3 & 0 & 1/3\end{matrix} \right] $=$ \left[ \begin{matrix}2 \\ 23 \\ 5\end{matrix} \right] $
Replacing the numbers by letters we get "BWE"
