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# Learn Financial Freedom Step by Step

Determinant is a square matrix but it is under to straight line instead two brackets. We can expand it and we can calculate its value. In simple words, a determinant is a single number associated to a square matrix. In short, we write determinant as det. A or | A | . Remember, non square matrices do not have determinants.

Calculation the value of Determinant  of order 2

| a11 a12 |

| a21 a22 |

a11 X a22 - a12 X a21

for example

(4 5)

( 56 )

it is sequare matrix, its deteminant det. A =

| 4 5 |

| 5 6 |

4 X 6 - 5 X 5 = 24 - 25 = -1

Determinant of order 3

if matrix is square matrix of order 3 X 3, its determinant is possible

a 11 a 12 a 13

a 21 a 22 a 23

a31 a 32 a33

= a 11 | a 22 a 23 | -  a 12 | a 21 a 23 |  + a 13 | a 21 a 22 |

| a32 a 33 |                | a31 a 33 |              | a31 a 32 |

Now apply determinant formula of 2 order

= a11 (  a22 X a33 - a23 X a32) - a 12 (  a21 X a33 - a23 X a31)  + a 13 (  a21 X a32 - a22 X a31)

In following example , you have given the value of matrix in two brackets and you have to calculate the value of determinant , just simple multiply each co-factor of first row to first row's elements and sum the results .

Importance of Calculating Determinant

Determinant is very useful for calculating inverse of matrix and adjoint of matrix . Because co-factor for adj. only calculate in determinant not in matrix .

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Svtuition: What is Determinant?
What is Determinant?