Code

/*
More details about transforms here: http://msdn.microsoft.com/en-us/library/system.windows.media.transform.aspx

ROTATE TRANSFORM (θ)
|+cosθ -sinθ 0|
|+sinθ +cosθ 0|

SCALE TRANSFORM (scale_x, scale_y)
|scale_x 0       0|
|0       scale_y 0|

SKEW TRANSFORM (skew_x, skew_y)
|1      skew_x 0|
|skew_y 1      0|
skew_x = tan(angle_x)
skew_y = tan(angle_y)

TRANSLATE TRANSFORM (offset_x, offset_y)
|1 0 offset_x|
|0 1 offset_y|

SCALE*ROTATE*TRANSLATE: // I prefer to using this one because rotating is more common than skewing
|+scale_x*cosθ -scale_y*sinθ offset_x|
|+scale_x*sinθ +scale_y*cosθ offset_y|

SCALE*SKEW*TRANSLATE:   // this one can be used on any matrix
|scale_x        scale_y*skew_x offset_x|
|scale_x*skew_y scale_y        offset_y|

assume: scale_x != 0 && scale_y != 0
so this code won't work if it's a singular matrix
*/
const float epsilon = 1e-4;
Console.WriteLine("<transforms>");
float ratio_a = _11 / _22;
float ratio_b = -(_21 / _12);       // if it is rotation, ratio_a=ratio_b=scale_x/scale_y
if (float_equals(ratio_a, ratio_b)) // SCALE*ROTATE
{
    // sqrt((scale_x*cosθ)^2+(scale_x*sinθ)^2)=sqrt(scale_x^2*cos^2 θ+scale_x^2*sin^2 θ)=scale_x*sqrt(cos^2 θ+sin^2 θ)=scale_x*sqrt(1)=scale_x
    float scale_x = Math.Sqrt(_11 * _11 + _21 * _21);
    float scale_y = Math.Sqrt(_12 * _12 + _22 * _22);
    float theta = Math.Acos(_11 / scale_x); // =acos(scale_x*cosθ/scale_x)=acos(cosθ)=θ
    if (Math.Abs(scale_x - 1) > epsilon || Math.Abs(scale_y - 1) > epsilon) Console.WriteLine("<scale factor='{0},{1}' />");
    if (Math.Abs(theta) > epsilon) Console.WriteLine("<rotate angle='{0}' />", theta);
}
else                                // SCALE*SKEW
{
    float scale_x = _11;
    float scale_y = _22;
    float skew_x = _12 / scale_y;
    float skew_y = _21 / scale_x;
    if (Math.Abs(scale_x - 1) > epsilon || Math.Abs(scale_y - 1) > epsilon) Console.WriteLine("<scale factor='{0},{1}' />");
    if (Math.Abs(skew_x) > epsilon || Math.Abs(skew_y) > epsilon) Console.WriteLine("<skew angle='{0},{1}' />", Math.Atan(skew_x), Math.Atan(skew_y));
}
if (Math.Abs(_13) > epsilon || Math.Abs(_23) > epsilon) Console.WriteLine("  <translate Offset='{0},{1}' />", _13, _23);    // *TRANSLATE
Console.WriteLine("</transforms>");

bool float_equals(float a, float b)
{
    return float.IsNaN(a) || float.IsNaN(b) || float.IsPositiveInfinity(a) && float.IsPositiveInfinity(b) || float.IsNegativeInfinity(a) && float.IsNegativeInfinity(b) || Math.Abs(a - b) < epsilon;
}