Calculate the Adjoint (Adjunct) and Determinant of a 2x2 or 3x3 square matrix.
Matrix Elements
a11
a12
a21
a22
Matrix Analysis
-2.00
Determinant |A|
Adjoint Matrix [Adj]
4
-2
-3
1
Inverse Matrix [A⁻¹]
-2.000
1.000
1.500
-0.500
About this calculator
Complexity of Matrices
The adjoint (or adjunct) of a square matrix is the transpose of its cofactor matrix. It plays a crucial role in finding the inverse of a matrix. Specifically, A⁻¹ = Adj(A) / |A|, provided the determinant is non-zero.
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Pro Tips
For a 2x2 matrix: swap diagonal elements and negate anti-diagonal elements.
If the determinant is zero, the matrix is 'singular' and has no inverse.
The adjoint matrix is always the same size as the original matrix.
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Fun Facts
"The term 'Adjoint' was first used by the mathematician Cauchy in 1841."
"Matrices are used in everything from 3D computer graphics to quantum mechanics."
"Google's original search algorithm, PageRank, is essentially a massive matrix calculation."
Formula: Adj(A) = [Cᵢⱼ]ᵀ (Transpose of Cofactor Matrix)
