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Question

Let A be the set of all 4×4 skew symmetric matrices whose entries are 1,0or1. If there are exactly four 0s, six 1s and six -1s then the number of such matrices is

A
64
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B
32
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C
0
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D
16
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Solution

The correct option is A 64
A is a skew-symmetric matrix of order 4X4.
For skew symmetric matrix aij=aji
So,let A=⎢ ⎢ ⎢ ⎢0abca0debd0fcef0⎥ ⎥ ⎥ ⎥
Each element above diagonal can be filled in 2 ways (1 or -1). And once an element above diagonal is filled, one element below will be negative of it.
total number of ways=26×16=64 ways .
( there are 6 elements above the diagonal and 6 below.)

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