Determinants
Definition of Determinants:
Let a11, a12, a21, a22 be any four numbers. The symbol 
represents the number a11a22 – a12a21 and is called determinants of order 2. The number a11, a12, a21, a22 are called elements of the determinant and the number a11a22 – a21a12 is called the value of determinant.
Minors, Cofactors and Adjoint
Cofactors
The minor Mij multiplied by (–1)i + j is called the cofactor of element aij . We shall denote the cofactor of an element by corresponding capital letter.
Adjoint
When all the elements of a matrix ‘A’ are replaced by its co-factor, then the transpose of that matrix is known as adjoint of matrix ‘A’.
aij →Cij
AdjA= [Cij ]T
Properties of adjoint matrix A(Adj A)
1. A x AdjA = |A| x I
2. A-1 = 1/ |A| x (AdjA )
Determinant of order n
- A determinant of order n has n-row and n-columns. It has n × n elements.
- A determinant of order n is a square array of n × n quantities enclosed between vertical bars.
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