Final answer:
Only statement C, which says that invertible matrices have an inverse matrix, is universally true. Statements A and D are specific cases and not generally true, and statement B is categorically false as a non-zero determinant is required for invertibility.
Step-by-step explanation:
When determining the characteristics of invertible matrices, we must identify which statements are intrinsically true. Firstly, it's important to note that invertible matrices are those that have an inverse matrix, which allows them to be multiplied by their inverse to get the identity matrix. With that in mind, here is a closer look at the provided statements:
A) have a determinant equal to 1: This is not necessarily true for all invertible matrices. While it's true that the determinant of an invertible matrix cannot be zero, it does not need to be 1. Any non-zero determinant indicates that a matrix is invertible.
B) have a determinant equal to 0: This statement is false. A matrix with a determinant of 0 is not invertible and thus cannot have an inverse. The determinant being zero indicates that the matrix is singular or degenerate.
C) have an inverse matrix: This statement is true. By definition, an invertible matrix is one that has an inverse, with which it can perform the operation of matrix multiplication yielding the identity matrix.
D) have a rank of 2: This statement is not always true. Invertible matrices can be of any size, not just 2x2. The rank of an invertible matrix must be full, meaning it is equal to the size of the matrix, but not specifically 2.
Therefore, only statement C) is universally true for all invertible matrices—such matrices must have an inverse.