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There are some properties of Determinants, which are commonly used
The value of the determinant remains unchanged if it’s rows and
columns are interchanged
(i.e. |𝐴 𝑇 | = |A|)
Check Example 6
If any two rows (or columns) of a determinant are interchanged then sign of determinant changes
Check Example 7
If all elements of a row (or column) are zero, determinant is 0.
If any two rows (or columns) of a determinant are identical, the value of determinant is zero.
Check Example 8 for proof
If each element of a row (or a column) of a determinant is multiplied by a constant k, then determinant’s value gets multiplied by k
Check Example 9
If elements of a row or column of a determinant are expressed as
sum of two (or more) terms,
then the determinant can be expressed as sum of two (or more) determinants.
Check Example 10 for proof
If in a determinant all the elements above or below the diagonal is
then value of the determinant is equal to product of the diagonal elements.