Final answer:
The question involves understanding the concept of an invertible matrix in linear algebra. It relates to the broader topic of solving equations and performing operations like finding inverses to 'undo' certain mathematical actions.
Step-by-step explanation:
If we suppose a is an invertible n x n matrix, we are discussing a concept in linear algebra, a branch of advanced mathematics often studied in college. An invertible matrix, also known as a nonsingular or nondegenerate matrix, is one that has an inverse such that when it is multiplied by its inverse it yields the identity matrix. In essence, the inverse matrix 'undoes' the actions of the original matrix. This is similar to solving for a in the Pythagorean theorem if we have a right triangle with sides b and c and we're trying to find side a, where we must 'undo' the square by taking the square root.
The questions in the student's prompt are exploring the processes of isolating variables and comparing equations. These are fundamental skills in algebra and are crucial when working with matrices and solving equations.