The number of all 3×3 matrices A , with entries from the set {-1,0,1} such that the  sum of the diagonal elements of AAT is 3 . is

trAAT=3a112+a122+a132+a212+………+a332=3∣ Possible cases 0,0,0,0,0,0,1,1,1→10,0,0,0,0,0,-1,-1,-1→10,0,0,0,0,01,1,-1  →30,0,0,0,0,0,-1,1,-1→3C6   9×8=84×8=672