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Powers of a matrix

An=A⋅A⋯A⏟nA^n = \underbrace{A\cdot A\cdots A}_{n}
AA
a square matrix
nn
the exponent

High powers of a structured matrix are found by computing the first few and reading off the pattern, not by repeated multiplication.

54
questions use it
29
of them past-year
2015–2026
years it has appeared
17%
rated HARD
4
exams
Matrices & Determinants notesOpen all 54 in the paper builder

Used alongside

How often each of these appears in the same solution as this one.

54 questions whose solution uses this

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

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Showing 54 of 54 questions — easiest first, then oldest paper first.

  • #1NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #2NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #3NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #4NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #5NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #6Maharashtra HSC Class 12 → Mathematics → Matrices → Elementary Transformations of a Matrix

  • #7NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #8NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #9NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #10CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #11CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #12NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #13NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #14CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #15NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #16CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #17NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #18NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #19NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #20NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #21NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #22NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #23NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #24NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #25NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #26CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #27NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #28Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #29NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #30NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #31NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial

  • #32NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #33NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #34NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #35NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #36NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #37CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #38CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #39CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #40CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #41CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #42CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #43CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #44CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #45NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #46NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #47NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #48NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #49NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #50NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #51MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #52MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #53MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #54MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

Every identity this chapter tests, with its own question set.

All Matrices & Determinants formulas