Alongside encryption and signatures, key agreement is one of the fundamental issues in modern cryptography and its security is the main concern in cloud computing and World Wide Web-based applications. In this paper, a novel type of more secure 3-pass key agreement protocol is proposed based on a recently proposed matrix-based key agreement protocol of Romańczuk and Ustimenko. By the hash-and-sign approach and immediate use of new session key, explicit key authentication, forward secrecy and bit security are achieved simultaneously. Cryptanalysis also shows that it is immune to the man-in-the-middle attack while matrix entries from a commutative ring provide an advantageous hiding mechanism.