The number a1 b2 – a2 b1
which determines uniqueness of solution is associated with the matrix 
1
1
2
2
A
a
b
a
b


= 



and is called the determinant of A or det A Determinants have wide applications in
Engineering, Science, Economics, Social Science, etc In this chapter, we shall study determinants up to order three only with real entries Also, we will study various properties of determinants, minors, cofactors and applications
of determinants in finding the area of a triangle, adjoint and inverse of a square matrix,
consistency and inconsistency of system of linear equations and solution of linear
equations in two or three variables using inverse of a matrix