Hello student,
Determinants can be solved quickly using the properties. These properties are extremely useful and help in reaching the answers easily and quickly.
One can either solve the determinant directly or use the Sarrus Rule. Sarrus Rule helps in finding the determinant quickly.
Then we have the properties of determinants which reduce the efforts involved in solving a question.
1. The determinant of square matrix whose one row (column) has all its elements as zeroes is 0.
2. In case of interchange of two rows, Det A* = - Det A, where A* is the new determinant.
3. If the entries in two rows are proportional, then Det = 0.
4. Suppose there is a matrix A and we get matrix B by multiplying a row(column) of A by scalar 's' and then adding it to another row (column). Then Det A) = Det(B).
These properties are extremely helpful and help in reaching results easily and quickly