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
convolution of RGB channel

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

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