A word on the reality of the internal implementation of the mutex lock deep within the kernel fabric: Linux tries to implement a fast path approach when possible.
A fast path is the most optimized high-performance type of code path; for example, one with no locks and no blocking. The intent is to have code follow this fast path as far as possible. Only when it really isn't possible does the kernel fall back to a (possible) "mid path", and then a "slow path", approach; it still works but is slow(er).
This fast path is taken in the absence of contention for the lock (that is, the lock is in an unlocked state to begin with). So, the lock is locked with no fuss, pretty much immediately. If, however, the mutex is already locked, then the kernel typically uses a mid path optimistic spinning implementation, making it more of a hybrid (mutex/spinlock) lock type. If even this isn't possible, the "slow path" is...
