Let P be a matrix of order 3 × 3 such that all the entries in P are from the set - 1 , 0, 1 . Then, the maximum possible value of the determinant of P is _______.

Step-by-step solution

∆ = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 = a 1 b 2 c 3 + a 2 b 3 c 1 + a 3 b 1 c 2 ⏟ x - a 3 b 2 c 1 + a 2 b 1 c 3 + a 1 b 3 c 2 ⏟ y Now if x ≤ 3 and y ≥ - 3 The ∆ can be maximum 6 but it is not possible because x = 3 ⇒ each term of x = 1 And y = -3 ⇒ each term of y = - 1 ⇒ ∏ i = 1 3 a i b i c i = 1   and ∏ i = 1 3 a i b i c i = - 1 , which is a contradiction. Now for value to be 5 one the terms must be zero but that will make two terms zero whic