How to rearrange rows in specific intervals

I have a matrix like so:

[x1  y1  z1;
x2  y2  z2;
x3  y3  z3;
x1  y1  z1;
x2  y2  z2;
x3  y3  z3;
x1  y1  z1;
x2  y2  z2;
x3  y3  z3]

Is there a non-loop solution to reorder the matrix to:

[x1  y1  z1;
x1  y1  z1;
x1  y1  z1;
x2  y2  z2;
x2  y2  z2;
x2  y2  z2;
x3  y3  z3;
x3  y3  z3;
x3  y3  z3]

In other words get every third column (in this case) and set them in order. The final matrix would end up being the same size.

I appreciate any help possible.

Answer 1

[Star Strider]

I use the Symbolic Math Toolbox to illustrate the approach and the desired result:

syms x1 y1 z1 x2 y2 z2 x3 y3 z3 real
M = [x1  y1  z1;
    x2  y2  z2;
    x3  y3  z3;
    x1  y1  z1;
    x2  y2  z2;
    x3  y3  z3;
    x1  y1  z1;
    x2  y2  z2;
    x3  y3  z3];

A = reshape(M, 3, 3, []);
B = permute(A, [3 2 1]);
Result = reshape(B, 3, [])'

Result =
[ x1, y1, z1]
[ x1, y1, z1]
[ x1, y1, z1]
[ x2, y2, z2]
[ x2, y2, z2]
[ x2, y2, z2]
[ x3, y3, z3]
[ x3, y3, z3]
[ x3, y3, z3]

Answer 2

[KSSV]

A = [1 2 3 ; 4 5 6 ; 7 8 9 ; 1 2 3 ; 4 5 6 ;7 8 9 ; 1 2 3 ; 4 5 6 ; 7 8 9] ;

[val,idx] = sort(A(:,1)) ;
B = A(idx,:)

[Alejandro]

What if the values of the matrix are not in order? suppose a random matrix.

[KSSV]

Same thing works.......provided the random matrix is given in the way the matrix is.

x1 = rand ; y1 = rand ;z1 = rand ;
x2 = rand ; y2 = rand ;z2 = rand ;
x3 = rand ; y3 = rand ;z3 = rand ; 
A = [x1  y1  z1; x2  y2  z2; x3  y3  z3; x1  y1  z1; x2  y2  z2; x3  y3  z3; x1  y1  z1; x2  y2  z2; x3  y3  z3] ;
[val,idx] = sort(A(:,1)) ;
B = A(idx,:)