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Idempotent matrices

A2=A  ⇒  Ak=A (k≥1)A^2 = A \;\Rightarrow\; A^k = A \ (k \ge 1)
kk
any positive integer

A matrix equal to its own square stays unchanged under every higher power, which collapses long expressions immediately.

17
questions use it
6
of them past-year
2022–2026
years it has appeared
24%
rated HARD
2
exams
Matrices & Determinants notesOpen all 17 in the paper builder

Used alongside

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

17 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 17 of 17 questions — easiest first, then oldest paper first.

  • #1NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #2CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

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

  • #4NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #6NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #8NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #9NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #10NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

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

  • #13CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #14NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #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 → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

All Matrices & Determinants formulas