Power of a Matrix A^n Shortcuts | JEE Main 2027 Maths (English)

Free notes + solved JEE problems for this lesson: https://rankdeterminant.com/go/yt-mat... This chapter:    • Mixed JEE Main-Pattern Problems | JEE Math...   All lessons of this unit:    • Matrices & Determinants | JEE Main 2027 Ma...   Find large powers of a matrix in JEE Main without long multiplication: the A squared = kA pattern and its k to the power n minus 1 trap, powers that cycle back to the identity matrix, and the topper's A = I + N trick with a nilpotent N and the binomial theorem. Two solved problems: the sum of all entries of A^10 and of A^50. Chapters 0:00 Introduction 0:36 Move 1: when A squared is a multiple of A 1:52 Move 2: a power that equals I 2:47 Topper's trick: write A=I+N 4:08 Example 1: sum of all entries of A^10 using A^2 = 2A 5:22 Example 2: sum of all entries of A^50 using A = I + N 7:03 Quick revision: A^2 = kA, A^m = I and A = I + N A free JEE paper every day and a full JEE Main mock every Sunday: https://rankdeterminant.com/go/yt-dai... Mathematics · Unit 3 · Matrices & Determinants · Chapter 5 · Mixed JEE Main-Pattern Problems #PowerOfMatrix #JEEMaths #JEE2027 Narrated with a computer voice.