Question

The number of different n×n symmetric matrices with each element being either 0 or 1 where n =5.

Answer 1

You have
`5` free entries along the diagonal. Since
`a_(ij)=a_(ji)`, you only need to worry about how many choices are available for the triangular part either above or below the diagonal. These parts both contain
`4+3+2+1=10` entries.

So the number of possibly symmetric binary matrices is
`2^5*2^(10)=2^(15)`.