Without expanding the determinant, prove that . SINGULAR MATRIX A square matrix is said to be singular if . Also, is called non singular if .
Without expanding the determinant, prove that . SINGULAR MATRIX A square matrix is said to be singular if . Also, is called non singular if .

Solution:

We know that , would not change anything for the determinant.
Applying the same in above determinant, we get
Now it can clearly be seen that
Applying above equation we get,

We know that if a row or column of a determinant is 0 . Then it is singular determinant.