How to replace values in a matrix based on specific indices? [duplicate]

Question

I'm trying to index a matrix based on an array of coordinates, so that I can replace the values in those positions with 1, and leave the rest as is. Here's what I mean:

I have the following 3x3 matrix

matrix = np.zeros((3,3), dtype=int)
matrix

>>> array([[0, 0, 0],
           [0, 0, 0],
           [0, 0, 0]])

and I have the following array

coords = np.array([[0,0],[2,1],[0,2]])
coords

>>> array([[0, 0],
           [2, 1],
           [0, 2]])

What I would like to do is replace the values in the original matrix with 1 only in the positions specified by the elements in the array coords. This is the desired output:

>>> array([[1, 0, 1],
           [0, 0, 0],
           [0, 1, 0]])

What I've tried to do is

matrix[coords]=1

However, this is the output I get:

>>> array([[1, 1, 1],
           [1, 1, 1],
           [1, 1, 1]])

Does anyone know how I can replace only the values in the positions specified, and obtain my desired output instead?

Thank you all for your help.