Explanation:

About the law commission of India
Statement 1 is correct: It is an executive body established by an order of the Government of India.

• Originally formed in 1955, the commission is reconstituted every three years and so far, 277 reports have been submitted to the government.
• The last Law Commission, under Justice B.S. Chauhan (retd.), had submitted reports and working papers on key issues such as simultaneous elections to the Lok Sabha and the Assemblies and a uniform civil code.

Composition

• Apart from having a full-time chairperson, the commission will have four full-time members, including a member-secretary.

Statement 2 is correct: Law and Legislative Secretaries in the Law Ministry will be the ex-officio members of the commission.

• It will also have not more than five part-time members.
• A retired Supreme Court judge or Chief Justice of a High Court will head the Commission.

Roles and functions

• The Law Commission shall, on a reference made to it by the Central Government or suo motu, undertake research in law and review of existing laws in India for making reforms and enacting new legislation.
• It shall also undertake studies and research for bringing reforms in the justice delivery systems for elimination of delay in procedures, speedy disposal of cases, reduction in cost of litigation, etc.

Hence both statements are correct.