Can I do an arbitrage trade between the two exchanges?

Arbitrage trading between two exchanges is a valid and legal trading strategy. In this type of trade, you take advantage of price differences between two exchanges. If the price of a stock is higher on one exchange and lower on another, you can buy on the cheaper exchange and sell on the more expensive one, pocketing the difference as profit. It's worth noting that this kind of trading is not without risks, though. There are latency and liquidity risks that can affect the profitability of your trades.

For Ex:

Scenario 1: Assume Eicher motor is trading on BSE at a price of 2500 and at the same time it is trading on NSE at 2504. Here you can create an arbitrage position as intraday position by buying on BSE at cheaper price and selling on NSE at expensive price and the difference of Rs. 4 (2504-2500) you can take as a profit. But during this transaction you also has to account the cost of transaction (Brokerage cost, Taxes etc.) otherwise you will end up with a loss.

Scenario 2: If you already have the same stock in your portfolio (considering you bought it from NSE) then also you can create an arbitrage. For this you have to sell the stock from your holding and immediately buy it from another exchange BSE. In this scenario the transaction cost will be reduced as you already have the stock in your portfolio.

Note: Always consider all the cost related to the transaction first. Then only create any position.