___________ are there only to determine matters of law did the trial court conduct its proceedings fairly and correctly.

The term you are looking for is "Appellate Courts."

Explanation:

Appellate courts exist to review the decisions of lower courts, focusing on issues of law rather than the facts of the case. Their primary role is to ensure that trials are conducted according to legal principles and that the rights of all parties are respected. They do not conduct trials or hear new evidence; instead, they examine the record from the original trial to determine whether there were errors in the application of the law, proper procedures followed, and whether the legal standards were met. If errors are found that could have affected the outcome of the case, appellate courts have the authority to reverse or modify the trial court's decision or order a new trial. This system of checks and balances is crucial for upholding justice and the rule of law.