Game-Based Learning (GBL) is a pedagogical methodology that focuses on the design, development, use and application of games in education and training [1]. GBL encourages active learning and engagement by providing students with possibilities to place problem solving in the context of games [2]. The GBL as an auxiliary tool in teaching mathematics allows the class to have a different dynamic in relation to teaching content and student learning. With the use of GBL, it is possible to raise students' curiosity and attention, classes become more pleasant and fun, and the topics are more interesting, making students much more motivated and more involved in learning the content [3]. Besides, it has an added advantage of facilitating the socialization between the students themselves since they interact while playing games.

GBL "Around the World with Matrices" is an innovative and attractive proposal that transforms learning Linear Algebra (LA) into a dynamic and collaborative experience. Its first application began in the 2023/2024 academic year [4], but in the meantime, it has undergone some changes and corrections related to the contents, the form of application, and includes a route designed by the students (secret route). In GBL New Edition, students of 2nd grade in a higher institution are invited to a virtual tour full of challenges and adventures. They are allowed to visit well-known cities from different countries by overcoming seven stages that combine mathematical knowledge with the emotion of a competition. Each level of the game is an opportunity for students to test and apply their knowledge of LA in a practical and fun way. Along the way, students must solve various problems and collect stars containing necessary letters to find the final word that ends the game. Students in each group of 4 will have to work together as a team, collaborate on solving challenges, and note down their findings in the logbook. This journey is not only part of the learning experience but also forms an important part of the assessment, as students are encouraged to reflect on the process and consolidate their knowledge.

Furthermore, GBL introduces an authorship element of creativity in challenging each team to create a secret stage that will later be integrated into the route of the next edition of GBL. Afterwards, this route is going to be shuffled, and teams will need to unravel the stages of others, hence, interaction and an exchange of knowledge will result. By the end, students not only revisit LA concepts in a fun way but also get actively involved in building a very special and collaborative educational experience.

What is the contribution of "Around the World with Matrices" to teaching and learning LA in Higher Education? GBL turns learning mathematics into a true adventure: It allows teamwork, critical thinking, and creativity, taking students through the amazing world of matrices. To get a qualitative and quantitative evaluation, several data were collected. The results show that the participants developed mathematical competencies and interpersonal and collaborative skills important for their academic and professional success, which evidences the efficiency of the game as a pedagogical tool. Thus, this research contributes to the discussion on new methodologies for teaching, pointing out the potentialities of digital technologies and GBL as allies in the educational process.

Keywords: Game based learning, higher education, mathematics, linear algebra, competencies.