What arguments did john marshall use to support his opinion in the case of marbury v. madison

The rulings in

Marbury v. Madison,

5 US 137 (1803) are related to the three questions posed to the Court:

1. Has the applicant a right to the commission he demands?

The Court determined that Marbury had a right to his commission, per An Act Concerning the District of Columbia that Congress passed in 1801, as well as Article II, Section 2, of the Constitution, which granted the President the right to make judicial nominations. Marbury's nomination had already been approved by the Senate, then signed an sealed by the former President, making it official.

2. If he has a right, and that right has been violated, do the laws of his country afford him a remedy?

Because the answer to the first question was that Marbury was properly appointed as a justice of the peace, his legal rights had been violated when Madison withheld the paperwork necessary to assume office.  

Further, the laws of the United States afforded Marbury a remedy to this violation.  

3. If they do afford him a remedy, is it a mandamus issuing from this court?

The Supreme Court determined it did not have original jurisdiction over the case, but appellate, and therefore could not issue a writ of mandamus. Marbury had to initiate legal action against Madison in the lower federal courts before the Supreme Court could review his case.  

This decision was based on the Court's determination that the Judiciary Act of 1789, in which Congress delegated to the Supreme Court original jurisdiction over cases involving the federal government, was partially unconstitutional because it granted the Court powers not specified by the Constitution.  

Part 3 of the Marbury decision established the high court's right of judicial review over legislation passed by Congress and the President, as well as the power to overturn laws deemed to be unconstitutional.

the constitution gives congress the power to regulate commerce "among" the several states.