Oral X : EXCELLENT exo CREATIF !

In this video, we solve an oral exam from the X-MP entrance exam on MATRICES, which also appeared at X-FUF in 2025. We are given a multiplicative function f from Mn(R) to R, i.e., such that for all matrices A, B, we have: f(AB) = f(A)f(B) / (A). We must show that A is invertible if and only if f(A) is non-zero. This will help develop your reflexes and creativity with matrices. 00:00 Introduction and problem statement 01:24 Hint 1 01:51 Solution: First implication 04:04 Hint 2 04:29 Solution: Nilpotent matrices 06:40 Hint 3 07:17 Solution: Using the rank 11:56 SUMMARY