What on earth do you mean by prove, If not within a system of proof?
You can prove the consistency of PBA, But you cannot prove that you cannot prove the inconsistency of PBA, because The inability to do both is the definition of consistency in the larger system.
You can prove the consistency of PBA, But you cannot prove that you cannot prove the inconsistency of PBA, because The inability to do both is the definition of consistency in the larger system.