If A is a 3 × 3 matrix and A = 2 , then 3 adj 3 A A 2 is equal to

Step-by-step solution

We need to find the value of 3 a d j 3 A A 2 We know that k A = k n A where n is the order of the matrix and k is a constant. ⇒ 3 A = 3 3 2 ⇒ 3 a d j 3 A A 2 = 3 3 a d j 3 3 · 2 A 2 We know that a d j k A = k n - 1 a d j A = 3 3 3 3 · 2 2 a d j A 2 Now we know that a d j A = A n - 1 = 3 3 3 3 · 2 2 3 a d j A 2 = 3 3 3 3 · 2 6 A 2 3 - 1 = 3 3 3 3 · 2 6 2 4 = 2 10 · 3 21 Hence, the required answer is 2 10 · 3 21 = 6 10 · 3 11