Determinant:

To every square matrix A = [aij] of order n, we can associate a number (real or
complex) called determinant of the square matrix A, where aij = (i, j)th element of A. This may be thought of as a function which associates each square matrix with a unique number (real or complex). If M is the set of square matrices, K is the set of numbers (real or complex) and f : M → K is defined by f (A) = k, where A ∈ M and k ∈ K, then f (A) is called the determinant of A.

It is also denoted by |A| or det A or Δ.

1. Determinant of Matrix of order One: 

A = [a] 

|A| = a 

2. Determinant of Matrix of order Two: 

3. Determinant of Matrix of order Three: