CMI 2021 Mathematics PhD Entrance | Linear Algebra Solution

Описание: Welcome to Prime Institute of Mathematics, Amravati!

In this video, we delve into an intriguing linear algebra problem from the CMI PhD Entrance Exam 2021. We will explore and analyze the following statements about a nonzero matrix A in M₂(R)

(A) If A²= 0 then (I₂- A)⁵ = 0
(B) If A²= 0then I₂- A is invertible
(C) If A³ = 0 then A² = 0
(D) If A² = A³ ≠0 then A is invertible

Our goal is to identify which of these statements are correct. This analysis will help you in deepen your understanding of linear algebra concepts.

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