Private Blockchains: Validation
How can Node B certify that block x is an invalid block
  


At a very basic level: a blockchain is a hash-linked list. Each block references the hash of the block preceding it, so any modification to a past block will be obvious, because that block's hash will no longer be a part of the longest chain. 

The situation is trickier for a new node that is hearing the history for the first time though, or during a time when there are two valid competing chain-tips. Which chain-tip should be considered valid? 

Bitcoin uses proof-of-work to decide which chain is valid: the one that has the most work accumulated (often termed 'the longest chain'). You cannot fake work being done, and so the competition amongst miners is what secures the network's history from tampering.

Without an objective measure (ie, energy spent creating a PoW), it can become very difficult to determine the valid chain in the event of a chain-split. You could create a system of voting, but such a system relies on subjective measures, and as such may be more game-able by network participants.