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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

Correct answer

24

Step-by-step solution

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

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