Problem 2542. Convert a grayscale image into RGB colour format, preserving data type

In the Image Processing Toolbox, MATLAB provides

rgb2gray

to convert a 3 channel color image into a 1 channel intensity (grayscale image). But not the other way around. Sometimes it is useful to have an intensity image represented in the 3 channel colour format.

Write a function to convert an input grayscale image into an equivalent RGB image, ensuring that the datatype of the input image matrix is preserved.

Example:

grayImg = [1 2 3; 4 5 6; 7 8 9];
rgbImg = gray2rgb(grayImg);
rgbImg(:,:,1) = [1 2 3; 4 5 6; 7 8 9];
rgbImg(:,:,2) = [1 2 3; 4 5 6; 7 8 9];
rgbImg(:,:,3) = [1 2 3; 4 5 6; 7 8 9];