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.