How is a convolution calculated on an image with three (RGB) channels?

Lets say we have a 3 Channel (RGB) image given by some matrix A

    A = [[[198 218 227]
          [196 216 225]
          [196 214 224]
          ...
          ...
          [185 201 217]
          [176 192 208]
          [162 178 194]]

and a blur kernal as

    K = [[0.1111, 0.1111, 0.1111],
         [0.1111, 0.1111, 0.1111],
         [0.1111, 0.1111, 0.1111]]

    #which is actually 0.111 ~= 1/9

The convolution can be represented as shown in the image below

As you can see in the image, each channel is individually convoluted and then combined to form a pixel.