How about doing it with Pillow:

from PIL import Image
img = Image.open('image.png').convert('L')
img.save('greyscale.png')

If an alpha (transparency) channel is present in the input image and should be preserved, use mode LA:

img = Image.open('image.png').convert('LA')

Using matplotlib and the formula

Y' = 0.2989 R + 0.5870 G + 0.1140 B 

you could do:

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as mpimg

def rgb2gray(rgb):
    return np.dot(rgb[...,:3], [0.2989, 0.5870, 0.1140])

img = mpimg.imread('image.png')     
gray = rgb2gray(img)    
plt.imshow(gray, cmap=plt.get_cmap('gray'), vmin=0, vmax=1)
plt.show()

You need to set the cmap properties of the imshow() function:

https://matplotlib.org/devdocs/api/_as_gen/matplotlib.pyplot.imshow.html

Use:

plt.imshow(img, cmap = "gray")

I frequently work with images as NumPy arrays - I do it like so:

import numpy as np
from PIL import Image

x=Image.open('im1.jpg','r')
x=x.convert('L') #makes it greyscale
y=np.asarray(x.getdata(),dtype=np.float64).reshape((x.size[1],x.size[0]))

<manipulate matrix y...>

y=np.asarray(y,dtype=np.uint8) #if values still in range 0-255! 
w=Image.fromarray(y,mode='L')
w.save('out.jpg')

If your array values y are no longer in the range 0-255 after the manipulations, you could step up to 16-bit TIFFs or simply rescale.

-Aldo