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Q.

Let A be the set of all 3×3 skew-symmetric matrices whose entries are either -1, 0, or 1 . If there are exactly three 0's, three 1's, and three (-1)'s, then the number of such matrices is ___________

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Detailed Solution

In a skew symmetric matrix, diagonal elements are zero

Also aij+aji=0 

Hence, number of matrices =2×2×2=8

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