Q.

How many 3X3 matrices M with entries 0,1,2 are there, for which the sum of the diagonal entries MTM is 5

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answer is 198.

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Detailed Solution

abcdefghiadgbehcfiSum of the diagonal elements a2+b2+c2+d2+e2+f2+g2+h2+i2=5case (i)  five ones and four zeros --- C9,5=126Case (ii) one 2 and one 1 -----2⋅C9,2=72total 198
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How many 3X3 matrices M with entries 0,1,2 are there, for which the sum of the diagonal entries MTM is 5