Adjoint Matrix (adj(A)): Definition and Calculation

I apologize for any confusion. The 'adj(A)' refers to the adjoint or adjugate matrix of A. The adjoint matrix is obtained by taking the transpose of the matrix of cofactors.

To find the adjoint matrix of A, you follow these steps:

1. Calculate the cofactor matrix: For each element in matrix A, calculate its cofactor. The cofactor of an element is the determinant of the matrix obtained by removing the row and column containing that element, multiplied by (-1) raised to the power of the sum of the row and column indices. The resulting cofactors form a matrix called the cofactor matrix.

2. Transpose the cofactor matrix: Take the transpose of the cofactor matrix. This means that the rows become columns and the columns become rows, resulting in the adjoint matrix.

The adjoint matrix is denoted as 'adj(A)' or sometimes 'adjugate(A)'.

Once you obtain the adjoint matrix, you can use it along with the determinant of A to calculate the inverse of A, as mentioned in the previous explanation.

I apologize for any confusion caused by the initial abbreviation.