Determinant of Matrix :
     The determinant of a square matrix is a single number calculated by combining all the elements of the matrix. Determinant of a matrix A is denoted by |A|. The Equation or Formula is calcuated as

Equation to calculate the determinant of 2x2 Matrix

|A|

=

.

a1 b1 a2 b2

.

=

a1xb2 - a2xb1

Equation to calculate the determinant of 3x3 Matrix

|A|

=

.

a1 b1 c1 a2 b2 c2 a3 b3 c3

.

=

a1 b1 c1 a2 b2 c2 a3 b3 c3

-

a1 b1 c1 a2 b2 c2 a3 b3 c3

+

a1 b1 c1 a2 b2 c2 a3 b3 c3

        The expansion of the determinant is..

|A|

=

.

a1 b1 c1 a2 b2 c2 a3 b3 c3

.

=

a1

.

b2 c2 b3 c3

.

- b1

.

a2 c2 a3 c3

.

+ c1

.

a2 b2 a3 b3

.

so |A|

=

.

A

.

=

a1(b2c3-c2b3) - b1(a2c3-c2a3) + c1(a2b3-b2a3)

                                                                                   
Thus we have to use the above formulas to calculate the value of determinant of the matrices.

Note: We can calculate the inverse of a matrix only when the determinant of that matrix is not equal to zero.