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Matrix polynomial equations

A2−(tr⁡A) A+∣A∣ I=O(2×2)A^2 - (\operatorname{tr}A)\,A + |A|\,I = O \quad (2\times2)
AA
a square matrix
tr⁡A\operatorname{tr}A
the trace, sum of diagonal entries
II
the identity matrix

A matrix satisfying a polynomial equation can be rearranged to give its inverse, its powers, or an unknown coefficient. For order two this is the Cayley-Hamilton relation.

46
questions use it
26
of them past-year
2018–2026
years it has appeared
24%
rated HARD
3
exams
Matrices & Determinants notesOpen all 46 in the paper builder

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

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

  • #3NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #5CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #6NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #7NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

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

  • #9NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #10NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #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

  • #14NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #16NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #18NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

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

  • #21MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #22CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #23CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #24CBSE Class 12 → Mathematics → Matrices → Elementary Operations and Inverse of a Matrix

  • #25CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #26MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #27CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #28CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #29MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

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

  • #31CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #32MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #33NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums

  • #34CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #35CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

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

  • #37NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #38NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #39NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #40NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #41NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #42MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #43MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #44MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #45MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #46MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

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

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