7.5. If $a, b, c, d, e, f, g, h, k$ are all 1 or -1, try to find the maximum possible value of
$$
a e k - a f h + b f g - b d k + c d h - c e g
$$
7.5. Since each term in the expression $a e k - a f h + b f g - b d k + c d h - c e g$ is either 1 or -1, the value of the expression is even. However, the expression cannot equal 6. If it did, then $a e k$, $b f g$, and $c d h$ would all have to be 1, making their product 1, while $a f h$, $b d k$, and $c e g$ would all have to be -1, making their product -1. But these two products should be equal, which is a contradiction. The value of the expression can be 4, for example, when $a=b=c=e=h=k=1$ and $d=f=g=-1$, the value of the expression is 4. Therefore, the maximum possible value is 4.