Formula

Determinant of the transpose

|A^T| = |A|

$A^T$: the transpose of A

Transposing a matrix leaves its determinant unchanged, which is why every row property of determinants has a matching column property.

questions use it

of them past-year

2017–2026

years it has appeared

13%

rated HARD

exams

Matrices & Determinants notes Open all 15 in the paper builder

Used alongside

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

15 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.

Filter

Showing 15 of 15 questions — easiest first, then oldest paper first.

#1NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#2NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#3NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#4CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#5CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#6NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#7NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#8NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#9NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#10CBSE Class 12 → Mathematics → Determinants → Area of a Triangle
#11CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#12NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#13CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#14NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
Set · 1 question
Consider the following for the next three (03) items that follow: Let $\Delta$ be the determinant of a matrix A, where $A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix}$ and $C_{11}, C_{12}, C_{13}$ be the cofactors of $a_{11}, a_{12}, a_{13}$ respectively.
- #15NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
  Strategy Concept notes

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

All Matrices & Determinants formulas