Let A be a $3\times 3$ matrix having entries from. the set {-1,0,1}. The number of all such matrices A having sum of all the entries equal to 5 , is

Case-I: $$\begin{gathered} 1\to 7\text{ times } \\ \text{ and }-1\to 2\text{ times } \end{gathered}$$

number of possible matrix = $\frac{9!}{7!2!}=36$

Case-II: $$\begin{gathered} 1\to 6\text{ times }, \\ -1\to 1\text{ times } \\ \text{ and }0\to 2\text{ times } \end{gathered}$$

number of possible matrix = $\frac{9!}{6!2!}=252$

Case-III: $$\begin{gathered} 1\to 5\text{ times } \\ \text{ and }0\to 4\text{ times } \end{gathered}$$

number of possible matrix = $\frac{9!}{5!4!}=126$

Hence total number of all such matrix A = 414