# Determinants: What is Determinant of a Matrix, Calculating the Determinant (For CBSE, ICSE, IAS, NET, NRA 2022)

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## What is Determinant of a Matrix?

- When a square matrix “A” of an order “n” is associated with a number, then it is titled as a determinant of the matrix.
- The determinant of a matrix is a
**special number**that can be calculated from a square matrix. - A Matrix is an array of numbers:

- The number involved in this square matrix can be a real number or a complex number.
- In the field of mathematics, Determinants can be used for a myriad of different calculations such as:
- Finding the area of a Triangle.
- Obtaining the solutions of linear equations in two or three variables.
- Solve Linear equations by using the inverse of a matrix
- Getting the adjoint and the inverse of a square matrix

## Calculating the Determinant

- First of all the matrix must be square (i.e.. have the same number of rows as columns) .
- Then it is just basic arithmetic.

## What Are the Properties of Determinants?

- The properties of determinants have its uses, in simplifying the evaluation by getting the maximum number of zeroes in a row or column.
- They hold true for determinants of any order.
- The determinant՚s value remains unchanged if the rows and columns are interchanged.
- For each element of a row or column which gets multiplied by a constant P, the value also gets multiplied by P.
- The sign of a determinant changes when any two rows or columns of a determinant are interchanged with each other.
- The value of a determinant is zero when any of the rows or columns of a determinant are identical to each other.
- The determinant obtained is a sum of two or more determinants if some or all elements of a column or a row are expressed as a sum of two or more terms
- When the equimultiples of corresponding elements are added, the value of the determinant remains the same, whenever the operation is multiplied.