Finding a Matrix Inverse with its Determinant and Adjoint

# Finding a Matrix Inverse with its Determinant and Adjoint

Recall that the adjoint of a matrix is the matrix of cofactors transposed. We will now look at an important theorem that relates the inverse of a matrix, its determinant, and its adjoint.

Theorem: If $A$ is an invertible matrix, that is $\det (A) ≠ 0$, then it follows that $A^{-1} = \frac{1}{\det(A)} \mathrm{adj}(A)$. |