Answer
$a \times b=b \times c =c \times a$
Work Step by Step
$a+b+c=0$ then $b=-a-c$
$a \times b=a \times (-a-c)=-a \times c$
$a \times b=c \times a$ ... (1)
$a+b+c=0$ then $a=-b-c$
$a \times b=(-b-c) \times b=-c \times b$
$a \times b=b \times c$ ...(2)
From equations (1) and (2), we have
$a \times b=b \times c =c \times a$
Hence,$a \times b=b \times c =c \times a$
