convolution and frequncy response
Convolution in the time domain means you are multiplying their frequency transforms. This is one of the many properties of the Fourier Transform.



Now, when you flip a signal X[n], you can also write it down as x[n1], where n1 = -n. If you look at the time scaling property, try replacing 'a' by -1. You'll observe that the F(W) will now become F(-W).

Since F(-W) is exactly the same as F(W), your result does not change.