If A = 2 1 - 1 3 5 2 1 6 1 , then t r A a d j a d j A is equal to (where, t r P denotes the trace of the matrix P i.e. the sum of all the diagonal elements of the matrix P and a d j P denotes the adjoint of matrix P )

Step-by-step solution

∴ a d j a d j A = A A (by property) A a d j a d j A = A A 2 … . . i A = 2 1 - 1 3 5 2 1 6 1 = 2 5 - 12 - 1 3 - 2 - 1 18 - 5 = - 14 - 1 - 13 = - 28 A 2 = 2 1 - 1 3 5 2 1 6 1 2 1 - 1 3 5 2 1 6 1 = 6 1 - 1 23 40 9 21 37 12 t r A a d j a d j A = t r A A 2 = - 28 6 + 40 + 12 = - 28 × 58 = - 1624