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# Learn Financial Freedom Step by Step

Here , I am giving you the full detail of properties of  determinant for your education purpose . The following properties are very helpful for student to calculate value of determinant without using of expending procedure .

Just remember and use following properties of determinants :-

## Value of Original Matrix's Determinant and its Transpose's Determinants will Always Equal

If we transpose of any matrix and then calculate the value of determinants, there is no difference between original value and transposed matrix’s determinant.

## 2. Value of Determinants will Zero, if its matrix One Column or Row is Zero

If all the elements of any one column or row of any matrix are zero, then the value of determinant must be zero.

## 3. Value of Determinants will Zero, if its matrix One Column or Row's all elements are equal

If any two rows or column’s all value are same then the value of determinant must be zero.

## 3. Value of Determinants will Zero, if its matrix any two Column or Row are proportionate

If any two rows or column of any matrix are proportionate, then the value of determinant must be zero.

## 4. value of determinant will also multiply with same scalar, If we multiply any row or column with any scalar

If we multiply any row or column with any scalar, its value of determinant will also multiply with same scalar.

## 5. Values of determinant never change if  take any common factor from any column and write outside the matrix

If take any common factor from any column and write outside the matrix then the values of determinant never change.

## 6. Values of determinant equal to the multiplication of its all main diagonals If we calculate the value of any diagonal matrix

If we calculate the value of any diagonal matrix then it always equal to the multiplication of its all main diagonals.

Following are the Scan images  of Example of  one Question which I have solved with the help of properties of determinant . I think this will be more helpful for you to understand properties .

## Ashok Kumar's Contents\$type=blogging\$show=https://www.svtuition.com/p/ashok-kumar.html\$hide=author

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Svtuition: What are the Properties of Determinants
What are the Properties of Determinants