Obtaining the Determinant and Inverse of a 3 x 3 Matrix

In section 9.1 we obtained the determinant of a 2 x 2 matrix. Below we will derive the determinant of a 3 x 3 matrix and then obtain the determinant of a general square matrix of dimension n x n.

The determinant of a 3x3 matrix A will be composed of all the elements of A. However, as we will see, the expression of the determinant of A will be reduced to particular expressions involving the determinants of certain 2x2 submatrices

9.2 OBTAINING THE DETERMINANT AND INVERSE OF A 3 , 3 MATRIX 371

of A. From a computational point of view, for the calculation of |/t |, we only have to remember how to compute the determinant of a 2 x 2 matrix. Let us denote the square matrix A of order 3 by

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