Rotate 2D square array

Problem

Rotate 2D n by n array to 90 degree clockwise and 90 degree anti-clockwise in-place.

e.g.

1 2 3    7 4 1
4 5 6 => 8 5 2
7 8 9    9 6 3

1 2 3    3 6 9
4 5 6 => 2 5 8
7 8 9    1 4 7

The trick is to do it in 2 steps.

Reverse whole array and then swap to symmetry

1 2 3    7 8 9    7 4 1
4 5 6 => 4 5 6 => 8 5 2
7 8 9    1 2 3    9 6 3

Reverse within and then swap to symmetry

1 2 3    3 2 1    3 6 9
4 5 6 => 6 5 4 => 2 5 8
7 8 9    9 8 7    1 4 7

Is the operation order important?

Swap to symmetry first and reverse whole array (Will become 90 anticlockwise)

1 2 3    1 4 7    3 6 9
4 5 6 => 2 5 8 => 2 5 8
7 8 9    3 6 9    1 4 7

Swap to symmetry first and reverse within (Will become 90 clockwise)

1 2 3    1 4 7    7 4 1
4 5 6 => 2 5 8 => 8 5 2
7 8 9    3 6 9    9 6 3

How about rotate 180 degree?

Reverse whole and reverse within

1 2 3    7 8 9    9 8 7
4 5 6 => 4 5 6 => 6 5 4
7 8 9    1 2 3    3 2 1

Reverse within and reverse whole (Same result)

1 2 3    3 2 1    9 8 7
4 5 6 => 6 5 4 => 6 5 4
7 8 9    9 8 7    3 2 1