For Diophantus (born probably sometime between AD 201 and 215; died aged 84, probably sometime between AD 285 and 299) Arithmetica, see :
A minus multiplied by a minus makes a plus; a minus multipliedby a plus makes a minus ; and the sign of a minus is a truncated $\Psi$ turned upside down, thus $\Lambda$ [with a third central leg]. [Footnote. The literal rendering would be "A wanting multiplied by a wanting makes a forthcoming."]
See also :
For subtraction alone is a sign used. The full term for wanting is λείψις as opposed to ύπαρξις, a forthcoming, which denotes a positive term. The symbol used to indicate wanting, corresponding to our sign for minus, is $\Lambda$ [with a third central leg]，which is described in the text as a ‘$\Psi$ turned downwards and truncated’.The description is evidently
interpolated, and it is now certain that the sign has nothing to do with $\Psi$.Nor is it confined to Diophantus, for it appears in practically the same form in Heron's Metrica [...].
Clearly, also if the rule is "correctly described", there is no hint to its modern symbolic formulation for lack of the modern symbols, that dates to the late 16th- early 17th Centuries.
For the modern version, see :
Unde patet ratio tum hujus regulae, $+$ in $+$ facit $+$; tum hujus $-$ in $+$ facit $-$. [...] Indeque patet ratio tum hujus regulae, $+$ in $-$ facit $-$; tum hujus, $-$ in $-$ facit $+$.
The "justification" is that to multiply a given quantity by a positive factor is ponendi ("ubi $+2$ significat bis ponere") while to multiply it by a negeative factor is tollendi ("ibidem $-2$ est bis tollere, seu bis ponere contrarium").
Contra vero, $-A$ per $-2$ multiplicare, est bis tollere $-A$, seu defectum $-A$ bis supplere, quod est $+A$ bis ponere, facitque $+2A$, (adeoque $-$ in $-$ facit $+$.)