Let A be a skew-symmetric matrix of order 3 . What is the value of det (4 A^4 )- det (3 A^3 )+ det (2 A^2 )- det (A)+ det (-I) Where I is the identity matrix of order 3 ?

Step-by-step solution

Given A is skew symmetric matrix of order 3 (odd) So | A |=0 Now, |4 A^4 |- |3 A^3 |+ |2 A^2 |-|A|+|-I| aligned & =4^3| ~A |^4-3^3| ~A |^3+2^2| ~A |^2-| A |+(-1)^3| I | & =0-0+0-0-1=-1 aligned