Assertion A : The system of equations x + y + z = 4, 2x - y + 2z = 5, x - 2y - z = 3 has unique solution. 

Reason R: If A is 3 x 3 matrix and B is a 3 x 1 non-zero column matrix. then the equation AX = B has unique solution if A is non-singular. 

In the light of the above statements, choose the most appropriate answer from the options given below:

(A) If each element in a row is a constant multiplier of corresponding element of another row of a determinant, then the value of the determinant is always non-zero.

(B) If each element on one side of the principal diagonal of a determinant is zero, then the value of the determinants the product of the diagonal elements.

(C) The value of determinant of skew symmetric matrix of odd order is always non-zero. 

(D) If A is non-singular matrix of order three, then $adj A=|A|^2$

(A) If A and B are symmetric matrices, then AB – BA is a skew symmetric matrix. 

(B) Multiplying a determinant by k means multiply elements of one column by k.

(C) If $A^2-A+I=0$ , then $A^-1$ is equal to A + I.

(D) If A and B are invertible matrices of same order, then $(A+B)^{-1}=B^{-1}+A^{-1}$. 

Choose the correct answer from the options given below: