If $\displaystyle A$ is a $\displaystyle 3 \times 3$ matrix with entries from the set $\displaystyle \left\{-1,1\right\}$. Then Total no. of non-singular matrices $\displaystyle A$ is
What did you do so far?
You can think of your problem as 3 (3x1)-vectors, which have to be linear independent. For the first vector, how many choices do you have? For any first vector, how many choices do you have for the second one? And then the third one?