Step 1: Recall what a microchip is.
A microchip, or integrated circuit, packs several transistors and other parts onto one piece of silicon so a circuit that once needed many parts fits on a tiny wafer.
Step 2: Match each name to its real work.
Jack Kilby worked at Texas Instruments and built the first working integrated circuit in 1958. Robert Noyce worked at Fairchild Semiconductor and built a more practical silicon-based chip in 1959, which could be made in bulk.
Step 3: Rule out the other names.
Larry Page and Sergey Brin built Google, a search engine, not hardware. Sabeer Bhatia built Hotmail, an email service. Gordon Moore co-founded Intel with Noyce and is known for Moore's Law, but the chip itself is credited to Kilby and Noyce, not Moore.
Final Answer:
Since Kilby and Noyce are jointly credited with inventing the microchip, option A is correct. \[ \boxed{\text{Robert Noyce and Jack Kilby}} \]