# Properties Of Determinants

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**Properties of Determinants:**

Basic properties of Detaerminants are given as follows:

1. If A is a square matrix then det (A) = det (A^{T}).

**Example-1:
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2. A is a square matrix. If we multiply a row or a column of a matrix by a real number u, then determinant of the matrix obtained equals the product of u and determinant of A.

**Example-2:
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3. If A is a square matrix with two identical row of column, the determinant det (A) = 0.

4. If A is square matrix with a zero row or zero column, then det (A) = 0.

5. If A is a traingular matrix then the determinant of A is the product of main diagonal elements.

6. If A and B are n n, det (AB) = det(A) det (B).

**Example-3:
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