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 _____.

JEE Advanced 2018 Mathematics question

Let be a matrix of order such that all the entries in are from the set . Then, the maximum possible value of the determinant of is .

Answer: 4

Solution

\det P=aei-afh-bdi+bfg+cdh-ceg, a sum of six terms each in . The product of these six signed terms is . If all entries are , this product is , so not all six terms can equal ; a

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Question ID VK-026797