Yes of course one can have demat and trading account with different broker.

When you buy shares, you can send the shares to the demat through multiple trading accounts. But while selling, you will be able to do so only through one trading account, the account for which you have the Power of Attorney (POA) mapped with the demat. POA is required to debit shares online when the shares are sold.

• If your a Speculator/Intraday Trader, Linking demat account to trading account (Different company) is advisable because buying and Selling will be done from the same Stock Broker.
• If your a Invester/Delivery Trader, I Strongly recommend you to open a new Demat account because you can buy shares through any trading account but to sell delivery shares you can sell through one trading account for which you have the POA mapped with the demat.