Determinants

1. For matrix A, \(|A|\) is read as determinant of A and not modulus of A.
2. Only square matrices have determinants.

4.2.1 Determinant of a matrix of order one

Let \(A=[a]\) be the matrix of order 1, then determinant of A is defined to be equal to a

4.2.2 Determinant of a matrix of order two

Let \(A=[\begin{smallmatrix}a_{11}&a_{12}\\ a_{21}&a_{22}\end{smallmatrix}]\) be a matrix of order \(2\times2\) of order 2 then the determinant of A is defined as: \(det(A)=|A|=\Delta=|\begin{smallmatrix}a_{11}&a_{12}\\ a_{21}&a_{22}\end{smallmatrix}|=a_{11}a_{22}-a_{21}a_{12}\)