Question

Suppose I have this matrix

8 3 1 1 2 2 1 1 1 1 1 1 2 2 1 1 3
3 8 3 1 1 2 2 1 1 1 1 1 1 2 2 1 1
1 3 8 3 1 1 2 2 1 1 1 1 1 1 2 2 1
1 1 3 8 3 1 1 2 2 1 1 1 1 1 1 2 2
2 1 1 3 8 3 1 1 2 2 1 1 1 1 1 1 2
2 2 1 1 3 8 3 1 1 2 2 1 1 1 1 1 1
1 2 2 1 1 3 8 3 1 1 2 2 1 1 1 1 1
1 1 2 2 1 1 3 8 3 1 1 2 2 1 1 1 1
1 1 1 2 2 1 1 3 8 3 1 1 2 2 1 1 1
1 1 1 1 2 2 1 1 3 8 3 1 1 2 2 1 1
1 1 1 1 1 2 2 1 1 3 8 3 1 1 2 2 1
1 1 1 1 1 1 2 2 1 1 3 8 3 1 1 2 2
2 1 1 1 1 1 1 2 2 1 1 3 8 3 1 1 2
2 2 1 1 1 1 1 1 2 2 1 1 3 8 3 1 1
1 2 2 1 1 1 1 1 1 2 2 1 1 3 8 3 1
1 1 2 2 1 1 1 1 1 1 2 2 1 1 3 8 3
3 1 1 2 2 1 1 1 1 1 1 2 2 1 1 3 8

I want to check

1. Off-diagonals are symmetric or not?(in above matrix, these are symmetric)

2. Elements occur in Off-diagonal (without repetition)?– in above matrix, these elements are 1,2,3

3. Elements in diagonal are symmetric? if yes print element? (like 8 in above matrix)

Answer 1

# 1
all(mat == t(mat))
[1] TRUE

# 2
unique(mat[upper.tri(mat) | lower.tri(mat)])
[1] 3 1 2

# 3
if(length(unique(diag(mat))) == 1) print(diag(mat)[1])
[1] 8