Let's first understand why we use the properties of the determinant. In some cases we must solve a matrix without the method of expansion(to find the determinant of the matrix). So we use the properties to solve the matrix.
Properties of the determinant of a matrix:
1. If the rows and columns of the determinant are interchanged, the value of the determinant remains unchanged.
2. If any 2 rows or 2 columns of a determinant are interchanged, the value remains same but the sign changes.
3. If each element of a row or column is multiplied by k, the whole determinant is multiplied by k.
4. If 2 rows or 2 columns of a determinant are identical, the value of determinant are identical, the value of determinant is 0.
5. If all the elements on 1 side of the principle diagonal are 0, then the value of the determinant is the product of principle diagonal elements.
Properties of the determinant of a matrix:
1. If the rows and columns of the determinant are interchanged, the value of the determinant remains unchanged.
2. If any 2 rows or 2 columns of a determinant are interchanged, the value remains same but the sign changes.
3. If each element of a row or column is multiplied by k, the whole determinant is multiplied by k.
4. If 2 rows or 2 columns of a determinant are identical, the value of determinant are identical, the value of determinant is 0.
5. If all the elements on 1 side of the principle diagonal are 0, then the value of the determinant is the product of principle diagonal elements.
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