On the other hand, there is a formula to find the adjoint of a 2×2 matrix without doing any calculations: Now we replace each element of matrix A by its cofactor to find the cofactor matrix of A:Īnd finally, we simply have to transpose the cofactor matrix: To do this, we have to apply the following formula: To compute the adjoint of matrix A, we first have to find the cofactor of each entry of the matrix. Let A be the following square matrix of order 2: We will first see the adjoint of a 2×2 dimension matrix, and then the adjoint of a 3×3 dimension matrix. Having seen the theory of the adjoint of a matrix, here are some solved examples of the calculation of the adjoint of a matrix. Note that the adjoint of a matrix can only be found for square matrices.
Where M ij is the i, j minor of the matrix, that is, the determinant that results from deleting the i-th row and the j-th column of the matrix. Remember that the formula to compute the i, j cofactor of a matrix is as follows:
To find the adjoint of a matrix, first replace each element in the matrix by its cofactor and then transpose the matrix.
