How did Blake and commissioner Gordon know Bruce Wayne was batman in 'the dark knight rises'?

In "The Dark Knight Rises," Blake deduces Bruce Wayne's identity as Batman through his keen observations and understanding of Wayne's character. He connects the dots when he realizes that Bruce is the only person who could operate as Batman given their shared ideals and moral compass. Commissioner Gordon, while not explicitly shown making the connection, has long suspected Bruce's dual identity, especially after years of working with him. The film implies a mutual understanding between them about Bruce's role as Gotham's protector.