Mathematics

The key insight is that invertibility is a very strong condition—it means $A$ has full rank and a unique inverse $A^{-1}$. Rather than checking each statement individually, think about what must follow logically from the existence of $A^{-1}$. Some properties (like being square, having nonzero determinant, or having linearly independent rows and columns) are equivalent to invertibility, while others are just coincidences that happen for specific matrices. Your job is to identify which property is guaranteed by the definition itself.

The key insight is that invertibility is a very strong condition—it means $A$ has full rank and a unique inverse $A^{-1}$. Rather than checking each statement individually, think about what must follow logically from the existence of $A^{-1}$. Some properties (like being square, having nonzero determinant, or having linearly independent rows and columns) are equivalent to invertibility, while others are just coincidences that happen for specific matrices. Your job is to identify which property is guaranteed by the definition itself.