Let A and B be two 3 × 3 matrices such that A B = I and A = 1 8 then a d j B a d j 2 A is equal to

Step-by-step solution

Given, A B = I and A = 1 8 Now by using property adj P Q = adj Q adj P we get, adj B · adj 2 A = adj adj 2 A adj B           . . . i Now adj adj 2 A = adj 2 A 2 = 2 A 4 = 2 3 4 A 4 = 2 3 4 A 4 = 8 4 A 4             . . . ii Property used adj A = A n - 1 and k A = k n A where n is order of matrix Now adj B = B 2   . . . . . . . . . . . . . ( i i i ) Now putting the value of equation ii   &   iii in eq i we get adj B · adj 2 A = 8 4 A