The determinant of a matrix A, Introduction to Determinant, calculating determinants

In the following we assume we have a square matrix (m=n). The determinant of a matrix A will be denoted by det(A) or |A|.

Determinant of a 2x2 matrix

Assuming A is an arbitrary 2x2 matrix A, where the elements are given by:

then the determinant of a this matrix is as follows:

Determinant of a 3x3 matrix

The determinant of a 3x3 matrix is a little more tricky and is found as follows ( for this case assume A is an arbitrary 3x3 matrix A, where the elements are given below)

then the determinant of a this matrix is as follows:

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