RO-TST 1987 Problem 1

Let $a,b,c$ be distinct real numbers such that $a+b+c>0$ . Let $M$ be the set of $3\times 3$ matrices with the property that each line and each column contain all given numbers $a,b,c$ . Find $\{\max \{ \det A \mid A \in M \}$ and the number of matrices which realise the maximum value.

Mircea Becheanu