Could somebody explain why?

[Arno K]

I am not that deep in this kind of mathematics, but I want to give it a try.
At first glance one awaits sine working on a matrix element by element which is wrong, only if your matrix is quadratic and diagonal this will hold. In your case you may try (exp(i*M)-exp(-i*M))/(2i) which exactly gives your result, you can do diagonalization yourself, for example via jordan(M)=[P,J]. Then M=P*J*P^-1 and so sin(M)=P*sin(J)*P^-1, this works as J is diagonal, and gives the same result, so the prime is correct. I tried Wolfram, but that handles matrices as lists of lists and this may be the reason for it returning the sine of the elements. So everything seems to be dependent on implementation, the 50G refuses an evaluation of transcendential functions on matrices. I think Bernard can give deeper explanation.
If you know what you need you can use apply(x->sin(x),m).
Arno