import torch
a, b = torch.rand((2,2)), torch.rand((2,2))

var1 = torch.sum(torch.abs((a * b)), 1)
print("L1 Distance is : ", var1)

var2 = torch.norm(((a * b)), 1, -1)
print("Torch NORM L1 Distance is : ", var2)

var3 = torch.sum(((a * b)) ** 2, 1).sqrt()
print("L2 SDistance is : ", var3)

var4 = torch.norm(((a * b)), 2, -1)
print("Torch NORM L2 Distance is : ", var4)

Your code was wrong.
L1 Distance is :  tensor([0.0924, 0.2528])
Torch NORM L1 Distance is :  tensor([0.0924, 0.2528])
L2 SDistance is :  tensor([0.0893, 0.2327])
Torch NORM L2 Distance is :  tensor([0.0893, 0.2327])