how can i rotate a square matrix?

Answer 1

mobaxus is right for 2x2
for 3x3 counterclockwise (ccw) rotating about the positive x-axis
use this matrix sequence.
1......0..........0
0....cosx...-sinex
0...sinex....cosx

3x3 ccw positive y-axis
cosx.....0.....sinx
0.........1..........0
-sinx....0......cosx

3x3 ccw psitive z-axis

cosx.....-sinx......0
sinx......cosx......0
0...........0..........1

All rotating through x angle
if it is clockwise change the signes.

Answer 2

Your question can be interpreted different ways :)

If you refer to rotating the numbers in the matrix itself: the following formula creates a matrix A' that is equal to the original matrix A but rotated 90 degrees clockwise:

A'(i, j) = A(n - j + 1, i)

where n is the number of rows and columns.

Answer 3

Have you got an old record player deck? If not, put your car on its side and use a wheel. However, remember to put the car back down on all four wheels after doing the matrix rotation as driving a car on its side is both illegal in most countries and extremely dangerous.

Answer 4

for a 2x2 matrix, use
cosx -sinx
sinx cosx
for a rotation of x degrees

Answer 5

By doing the transpose 2 times (inverting the lines and columns)
A =
a11, a12
a21, a22
-> (first transpose) =
a11, a21
a12, a22
->(second transpose) =
a11, a12
a21, a22