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Question

The number of 4×4 skew symmetric matrices that can be formed using exactly four 0's, six 3's and six 3's is

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Solution

For skew symmetric matrix aij=aji and diagonal elements =0
Let A be the matrix then
A=⎢ ⎢ ⎢ ⎢0abca0debd0fcef0⎥ ⎥ ⎥ ⎥
Each element above diagonal can be filled in 2 ways either 3 or 3.
The number such matrix possible
=26=64

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