## Quick Reference

The adjoint of a square matrix **A**, denoted by adj **A**, is the transpose of the matrix of cofactors of **A**. For **A**=[*a*_{ij}], let *A*_{ij} denote the cofactor of the entry *a*_{ij}. Then the matrix of cofactors is the matrix [*A*_{ij}] and adj **A**=[*A*_{ij}]^{T}. For example, a 3×3 matrix **A** and its adjoint can be written In the 2×2 case, a matrix **A** and its adjoint have the form The adjoint is important because it can be used to find the inverse of a matrix. From the properties of cofactors, it can be shown that **A** adj **A**=(det **A**)**I**. It follows that, when det **A** ≠ 0, the inverse of **A** is (1/det **A**) adj **A**.

*Subjects:*
Mathematics.