I put some money in Bitforex and some say that they do wash trading. This is where they inflate the volume of trade in their sites.
Is it legal? Also, what's the jurisdiction of Bitforex?
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According to Wikipedia:
A wash trade is a form of market manipulation in which an investor simultaneously sells and buys the same financial instruments to create misleading, artificial activity in the marketplace. First, an investor will place a sell order, then place a buy order to buy from himself, or vice versa.
Wash trading has been illegal in the United States since the passage of the Commodity Exchange Act (CEA), of 1936.
It is also regulated under the US Securities and Exchange Act of 1934, administered by the Securities and Exchange Commission (SEC). Section 10(b) and matching SEC rule SEC Rule 10b-5 have broad anti-fraud provisions.
15 U.S. Code § 78j says:
It shall be unlawful for any person, directly or indirectly, by the use of any means or instrumentality of interstate commerce or of the mails, or of any facility of any national securities exchange—
(b) To use or employ, in connection with the purchase or sale of any security registered on a national securities exchange or any security not so registered, or any securities-based swap agreement  any manipulative or deceptive device or contrivance in contravention of such rules and regulations as the Commission may prescribe as necessary or appropriate in the public interest or for the protection of investors.
According to this press release from the US SEC
“Wash trading is an abusive practice that misleads the market about the genuine supply and demand for a stock,” said Thomas J. Krysa, Associate Director of Enforcement in the SEC’s Denver Regional Office. “In this case, we allege that Pollack engaged in this type of trading, and he and his firm acted as unregistered brokers outside the boundaries of the law by effecting transactions in securities and avoiding SEC oversight and examinations that protect the interests of investors.”
In that case the US SEC alleged violations of Sections 15(a)(1), 9(a)(1), and 10(b) of the Securities and Exchange Act of 1934, and SEC rules 10b-5(a) and 10b-5(c).
So yes, it is illegal in the US. I don't know about other countries, but I wouldn't be surprised if it illegal in at least some other places.
There is a different but related practice known as a "wash sale". In this practice a security is sold in order to realize a loss (or less often a gain), and then the same security is repurchased, leaving the investment position the same as it was before the sale. In a wash sale the actual sale is to a legitimate third party. A wash sale, unlike wash trading, is not illegal in the US (nor anywhere that I know of). However in the US if the repurchase is within 30 days of the sale, the loss is not valid for tax purposes that year. The UK and some other countries have similar tax treatments of short-term wash sales. See wash-sale rule on Investopedia.