Abstract: Proofs play a prominent role in understanding linear algebra concepts that are undoubtedly abstract. In this talk, we will examine the structure of linear algebra proofs and their nature. We will also explore the existing structure that connects and condenses powerful ideas. In particular, we show the visual power of matrices and their role in building, capturing, and condensing abstract ideas. A natural and familiar structure that is built in Rn is not limited and does not fall apart. We will conclude with some instructional insights from our experiences teaching proof-based second courses in linear algebra. This talk is in collaboration with Judi McDonald from Washington State University