Pad a matrix with its sums Challenge:
Given a square input matrix \$A\$, pad the matrix with one row and one column on all four sides.

The value of each element in the top and bottom row should be the sum of the elements in each corresponding column.
The value of each element in the left and right column should be the sum of the elements in each corresponding row.
The value of the elements in the top left, and bottom right corner should be the sum of the elements on the diagonal
The value of the elements in the top right, and bottom left corner should be the sum of the elements in the anti-diagonal.

Example:
A = 
1   5   3
3   2   4
2   5   5

Output:
 8    6   12   12    7
 9    1    5    3    9
 9    3    2    4    9
12    2    5    5   12
 7    6   12   12    8

Explanation:
The top left and bottom right elements are the sum of the diagonal \$1+2+5=8\$. The top right and bottom left elements are the sum of the anti-diagonal \$2+2+3=7\$.
The top and bottom row (except the corners) are the sum of each of the columns in \$A\$: \$1+3+2=6\$, \$5+2+5=12\$ and \$3+4+5=12\$. Similarly, the left and right column (except the corners) are the sum of each of the rows of \$A\$: \$1+5+3=9\$, \$3+2+4=9\$ and \$2+5+5=12\$.
Input:

A non-empty square matrix, with non-negative integers.
Optional format

Output:

The matrix padded as explained above
Optional format, but it must be the same as the input format

Test cases:
Use the submissions in this challenge if you want to convert the input format to a more suitable one (for instance [[1, 5],[0, 2]]).
0
----------------
0 0 0
0 0 0
0 0 0


1 5
0 2
----------------
3 1 7 5
6 1 5 6
2 0 2 2
5 1 7 3


17   24    1    8   15
23    5    7   14   16
 4    6   13   20   22
10   12   19   21    3
11   18   25    2    9 
----------------
65   65   65   65   65   65   65
65   17   24    1    8   15   65
65   23    5    7   14   16   65
65    4    6   13   20   22   65
65   10   12   19   21    3   65
65   11   18   25    2    9   65
65   65   65   65   65   65   65


15    1    2   12
 4   10    9    7
 8    6    5   11
 3   13   14    0
----------------
30   30   30   30   30   30
30   15    1    2   12   30
30    4   10    9    7   30
30    8    6    5   11   30
30    3   13   14    0   30
30   30   30   30   30   30


This is code-golf, so the shortest solution in each language wins. Explanations are highly encouraged.
Jelly, 27 bytes

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