Matthew 3:13-17 - Why was Jesus baptised? Why did He undergo a baptism of repentance when He had no sin to repent of?

He was baptised as our representative. He was baptised to demonstrate His commitment to being our substitute, to taking upon Himself our sins and taking our punishment.

Furthermore, He was baptised to "fulfill all righteousness". Again He wasn't baptised to earn a righteousness for Himself, but rather to meet the demands of the law so that we could receive a perfect righteousness from Him through faith and so be justified before God.

The effectiveness of this work is displayed in the pleasure the Father shows in His Son - a pleasure which He has in us as we put our trust in Him.