How do I matricise a column/vector (applying a function like sum/diff/boolean)?

I have a vector, say

1
0
1
1
1
0

denoting gender. I want to matricise this vector into an square matrix and for every pair perform a function. So say I want to sum.

2 1 2 2 2 1
1 0 1 1 1 0
2 1 2 2 2 1
2 1 2 2 2 1
2 1 2 2 2 1
1 0 1 1 1 0

Or if the rule is ‘similar is a 1’

1 0 1 1 1 0
0 1 0 0 0 1
1 0 1 1 1 0
1 0 1 1 1 0
1 0 1 1 1 0
0 1 0 0 0 1

How can I create such a square matrix from a vector/column c(1,0,1,1,1,0)?

I have been manipulating numerous vectors but I keep on getting errors.