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Question:

Let A be the set of all 3x3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A is?

6

3

9

12

Solution:

If two zeros are the entries in the diagonal, then 3C2 × 3C1. If all the entries in the principle diagonal is 1, then 3C1 ⇒ Total matrix = 12.