Proof has a prominent place in the linear algebra curriculum, teaching and learning but in first-year courses it continues to be challenging for both instructors and students. While an introduction to new concepts through definitions and theorems adds to the complexity of the course, proof remains the number one hurdle for many students. How do students view proof in linear algebra? Do they distinguish argumentation and proof, and if so how? are among many questions that are still unanswered. Although research on proof in mathematics education is increasing, systematic studies on proof in linear algebra are still scarce. In this study, we examined responses to a set of interview questions on proof by a group of 16 first-year undergraduate students shortly after their final examination. This paper opens the case for a pedagogy of proof in linear algebra and examines students' reactions to, and voices on, proof in a first-year course in linear algebra. In particular, it addresses areas such as student views on understanding of proof, the purpose of a proof, and when and how proofs communicate to them. We employed Tall's Three Worlds as well as Harel's intellectual need to analyse the data. Although, these models are often applied to what students construct, we argue they can also be applied to how students perceive proofs. The results revealed that understanding a proof in order to gain personal conviction was a major concern of students.