This sentence uses 間違える (the transitive verb).
間違う is intransitive, but can also be used in this situation, right? It would also mean “He made a mistake.” But, would it have more of a connotation of “He is mistaken”?
@ericaw
“He is mistaken” is closer to 彼は間違っている or 彼は勘違い (kanchigai) している.
I usually translate 彼は間違えた as “He made a mistake” (transitive verb in past tense). – 彼は間違えた doesn’t necessarily means that he is still mistaken and doesn’t admit it.