​question 8
Q.8. 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 ________.

Dear Student,
Please find below the solution to the asked query:

=a1a2a3b1b2b3c1c2c3On expansion we get=a1b2c3-b3c2-a2b1c3-b3c1+a3b1c2-b2c1=a1b2c3-a1b3c2-a2b1c3+a2b3c1+a3b1c2-a3b2c1As there are 6 terms and each element of matrix is from set -1,0,1hence maximum value can be 6 , when all six terms are 1Value can be 6 when a1=1, a2=-1, a3=1, b2c3=b1c3=b1c2=1b3c2=b3c1=b2c1=-1b2c3b3c1b1c2=-1 and b1c3b3c2b2c1=-1which givesb1b2b3c1c2c3=-1 and 1which is not possible.

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3^9 .i.e.19683 you can sove it by block method of permutations
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