What are the properties of determinants in NCERT Class 12?
Answer (1)
Determinants possess several key properties that simplify their manipulation. Some of the important properties are:
- The determinant of the identity matrix is always 1.
- If two rows or columns of a matrix are interchanged, the sign of the determinant changes.
- If a row or column is multiplied by a constant, the determinant is also multiplied by that constant.
- Additionally, if any row or column of a matrix is entirely zero, the determinant of that matrix is zero.
- For triangular matrices (both upper and lower), the determinant is simply the product of the diagonal elements.
- Another important property is that the determinant of the product of two matrices equals the product of their individual determinants.
- These properties make it easier to compute and analyze determinants in different scenarios.
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