![]() ![]() ![]() This is sometimes referred to as the adjoint matrix. If such a matrix exists, we say that matrix is invertible. The final result of this step is called the adjugate matrix of the original. The inverse of (denoted by ) is an × matrix that satisfies, , where is the × identity matrix.They are indicators of keeping (+) or reversing (-) whatever sign the number originally had. ![]() Note that the (+) or (-) signs in the checkerboard diagram do not suggest that the final term should be positive or negative. Continue on with the rest of the matrix in this fashion. The third element keeps its original sign. For matrix A, the inverse of the Matrix is -1. When assigning signs, the first element of the first row keeps its original sign. In this article, we have gone through various details of the Adjoint and Inverse of a Matrix.You must then reverse the sign of alternating terms of this new matrix, following the “checkerboard” pattern shown. Thus, the determinant that you calculated from item (1,1) of the original matrix goes in position (1,1). The classical adjoint, or adjugate, of a square matrix A is the square matrix X, such that the (i,j)-th entry of X is the (j,i)-th cofactor of A. Place the results of the previous step into a new matrix of cofactors by aligning each minor matrix determinant with the corresponding position in the original matrix. ![]()
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