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 Main Mathematics question

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

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

The diagonal entries of are the sums of squares of the columns, so their total is the sum of the squares of all nine entries, which must equal . The squares of the allowed entries are ; a total of

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Question ID VK-020852