Properties Of Determinants

Concept: For a square matrix of order , an important property of determinants and adjoint matrices is: where:
• is an matrix
• is the adjoint (adjugate) of matrix
• represents the determinant of matrix Thus, the determinant of the adjoint matrix depends on the determinant of the original matrix and the order of the matrix.

Step 1: Identify the order of the matrix. The matrix is given as a matrix. Therefore,

Step 2: Use the determinant property of adjoint matrices. Using the formula: Substitute and :

Step 3: Compute the value. Thus,