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Technique

Counting matrices

orders of N entries=d(N),fillings=c mn\text{orders of } N \text{ entries} = d(N), \qquad \text{fillings} = c^{\,mn}
d(N)d(N)
the number of divisors of N
cc
choices available per entry

The possible orders of a matrix with a fixed number of entries correspond to the divisors of that number, and each position is then filled independently.

12
questions use it
9
of them past-year
2017–2025
years it has appeared
17%
rated HARD
3
exams
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  • #1NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #3CBSE Class 12 → Mathematics → Matrices → Order and Types of Matrices

  • #4CBSE Class 12 → Mathematics → Matrices → Order and Types of Matrices

  • #5NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #7CBSE Class 12 → Mathematics → Matrices → Symmetric and Skew-Symmetric Matrices

  • #8CBSE Class 12 → Mathematics → Matrices → Order and Types of Matrices

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

  • #10CBSE Class 12 → Mathematics → Matrices → Order and Types of Matrices

  • #11NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums

  • #12MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

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