Can I do an arbitrage trade between the two exchanges?

Yes it is possible to do an arbitrage trade since SEBI has mandated interoperability across exchanges. Hence shares bought in one exchange can be sold on other exchanges. This gives an arbitrage opportunity.

Let us understand this with an example:

Assume ITC stock is trading on NSE at 200 and on BSE at 204. You can do an arbitrage trade intraday, where you can buy on NSE at 200 and sell on BSE at 204 thus making a profit of Rs.4 per share.

Please note that the above example does not include Brokerage and other regulatory fees levied by your broker. Your actual profit will be net of such costs for both Buy and Sell.