For the matrix `A=[[1, 5],[ 6, 7]]`, verify that.
(i) `(A+A^(prime))`is a symmetric matrix
(ii) `(A-A^(prime))`is a skew symmetric matrix

Explanation

Given
`A=[[1, 5],[ 6, 7]]`
`therefore` `A'=[[1,6],[5,7]]`
(i) `A+A'=[[1, 5],[ 6, 7]]+[[1,6],[5,7]]=[[2,11],[11,14]]`

`(A+A')'=[[2,11],[11,14]]`
since
`(A+A')'=A+A'`
Hence, `A+A'` is a symmetric matrix.
(ii) `A-A'=[[1, 5],[ 6, 7]]-[[1,6],[5,7]]=[[0,-1],[1,0]]`
`(A-A')'=[[0,1],[-1,0]]=-[[0,-1],[1,0]]=-(A-A')`
Since, `(A-A')'=-(A-A')`

Hence, `(A-A')`is a skew-symmetric matrix.