The number of all $3*3$ $$ matrices, $A$ $$ , with enteries from the set $$ $\{-\mathrm{1,0},1\}$ such that the sum of the diagonal elements of $A{A}^{\mathrm{?}}$ ${}^{}$ is 3 , is(Matrices)

Let A=[a??]???. tr(AA?)=3.
Σa??² = 3.
Possible cases for non-zero elements are (1,1,1) or (-1,-1,-1) or (1,1,-1) etc.
Total combinations = ?C? * 2³ = 84 * 8 = 672.C? * 2³ = 84 * 8 = 672.