When the RSA algorithm is used for signing a message from Alice to Bob, which statement best describes that operation?

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When the RSA algorithm is used for signing a message from Alice to Bob, which statement best describes that operation?

A. Alice signs the message with her private key, and Bob verifies that signature with Alice's public key.
B. Alice signs the message with her public key, and Bob verifies that signature with Alice's private key.
C. Alice signs the message with Bob's private key, and Bob verifies that signature with his public key.
D. Alice signs the message with Bob's public key, and Bob verifies that signature with his private key.
E. Alice signs the message with her public key, and Bob verifies that signature with his private key.
F. Alice signs the message with her private key, and Bob verifies that signature with his public key.