The total number of $3 \times 3$ matrices $A$ having entries from the set $\{ 0,1,2,3 \}$ such that the sum of all the diagonal entries of $A A ^ { T }$ is 9 , is equal to $\_\_\_\_$.
The total number of $3 \times 3$ matrices $A$ having entries from the set $\{ 0,1,2,3 \}$ such that the sum of all the diagonal entries of $A A ^ { T }$ is 9 , is equal to $\_\_\_\_$.