For any real, square and non-singular matrix B , the det B-1 is

Q. For any real, square and non-singular matrix B , the det B^-1 is

(A) zero          

(B) (det B)^-1   

(C) -(det B)  

(D) det B

Ans: (det B)^-1

Sol:

For any matrix whose inverse exists i.e. non-singular

BB-1 = I

|BB^-1| = 1

|B||B^-1| = 1

det (B^-1) = (det B)^-1