The number of all possible symmetric matrices of order 3×3 with each entry 1 or 2 and whose sum of diagonal elements is equal to 5, is

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Correct answer: 24. Since, trace is equal to 5⇒ diagonal elements are 1,2,2 ∵ Matrix is also symmetric Therefore, possible number of such matrices =(3!)/(2!)×2^3=3×8=24

The number of all possible symmetric matrices of order $3 \times 3$ with each entry $1$ or $2$ and whose sum of diagonal elements is equal to $5,$ is

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