How many 3 3 matrices M with entries from 0,1,2 are there, for which the sum of the diagonal entries of M^TM is 5?

JEE Advanced 2017 Mathematics question

How many matrices with entries from are there, for which the sum of the diagonal entries of is 5?

(A)126
(B)198Correct
(C)162
(D)135

Answer: (B)

Solution

The -th diagonal entry of is the sum of squares of the entries in column , so the trace equals the sum of the squares of all nine entries. Entries are 0, 1 or

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Question ID VK-026686