If you have a matrix equation, the determinant is used to determine whether or not there are any solutions to the matrix equation - there will only be solutions when the determinant is not zero.
Every SQUARE matrix can be associated to an expression or a number which is called its determinant. If A = [ aij] is a square matrix of order n, then the determinant of A is denoted by det A OR |A|
Determinant is a way of expressing an expression. For example: a*d-b*c is defined as determinant which is written as
The children may ask as to why do we need to express the expression as a determinant, the answer is that we need it for solving equations as well as it has other applications in geometry.
A determinant of a matrix of order three is written as
a b c
d e f = a ( ei-hf) – b(di-fg)+c(dh-eg) = aei +bfg + cdh – ceg – bdi - afh
g h i