Applied Mathematics · Ch 2 — Algebra

Adjoint of a Matrix

2.6.3

Adjoint of a Matrix

The adjoint of a square matrix $A$ , written $\text{adj}\,A$ , is formed by first replacing every element of $A$ with its own cofactor (giving the cofactor matrix), and then taking the transpose of that cofactor matrix.

Two properties of the adjoint are used repeatedly, especially when finding an inverse:

A\,(\text{adj}\,A) = (\text{adj}\,A)\,A = |A|\,I

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← Previous · 2.6.2Example 23 — Find minors and cofactors of the elements of the determinant A = 2 -3 …Next · 2.6.3 →Example 24 — Find k, if A = -2 3 k 4 is a singular matrix.