If A , B are two non-singular matrices of order 3 and I is an identity matrix of order 3 such that A A T = 5 Ι and 3 A - 1 = 2 A T - A a d j 4 B , then B 2 is equal to (where A T and a d j A denote transpose and adjoint matrices of the matrix A respectively)

Step-by-step solution

A A T = 5 Ι ⇒ A 2 = 5 3 ….(1) 3 A - 1 = 2 A T - a d j 4 B Multiplying by A on both sides, we get 3 Ι = 2 A A T - A a d j 4 B ⇒ A 2 a d j 4 B = 7 Ι A 2 a d j 4 B = 7 3 5 3 4 6 B 2 = 7 3 (using (1)) B 2 = 7 3 5 3 ⋅ 4 6