Properties of Determinant

Before you see this post,

see

Determinant of Matrix

1. det [cA] = c^n det A

2. DETERMINANT of A MATRIX 

that is multiplied constants at a column of a certain matrix

 and added same column of another matrix 

3. determinant of exchanged 2 columns of matrix

If a_ik=a_il, where i=1,2, ... ,n, 

that means col_k [A] = col_l [A],

det A = det C.

So, det A = - det A.

Then, det A = 0.