Transpose of a 3D Tensor

Question

I'm finding it difficult to wrap my head around how the transpose operation works for Tensors of Rank 3 and above.

Here's an example in PyTorch

I was doing a transpose of tensors of rank 3 and according to transpose rule for rank 2 tensors which follow simple 2D matrix transpose rule. $$ {A_{ij}}^T =A_{ji} $$ But when I transposed a rank 3 tensor I ended up with a different output given below.
Can someone explain to me how is this happening?

a = torch.tensor(
        [[[1., 1., 1.],
         [1., 1., 1.],
         [1., 1., 1.]],

        [[0., 0., 0.],
         [0., 0., 0.],
         [0., 0., 0.]],

        [[1., 1., 1.],
         [1., 1., 1.],
         [1., 1., 1.]]])

Printing the tensor and the shape gives the following:

print(a)
print(a.shape)
tensor([[[1., 1., 1.],
         [1., 1., 1.],
         [1., 1., 1.]],

        [[0., 0., 0.],
         [0., 0., 0.],
         [0., 0., 0.]],

        [[1., 1., 1.],
         [1., 1., 1.],
         [1., 1., 1.]]])
torch.Size([3, 3, 3])

Transposing with a.T we get

tensor([[[1., 0., 1.],
         [1., 0., 1.],
         [1., 0., 1.]],

        [[1., 0., 1.],
         [1., 0., 1.],
         [1., 0., 1.]],

        [[1., 0., 1.],
         [1., 0., 1.],
         [1., 0., 1.]]])

Edit: As suggested I'm adding another example with unique values for every entry.
Tensor b

tensor([[[ 1.,  2.,  3.],
         [ 4.,  5.,  6.],
         [ 7.,  8.,  9.]],

        [[10., 11., 12.],
         [13., 14., 15.],
         [16., 17., 18.]],

        [[19., 20., 21.],
         [22., 23., 24.],
         [25., 26., 27.]]])

Transpose of Tensor b ( b.T)

tensor([[[ 1., 10., 19.],
         [ 4., 13., 22.],
         [ 7., 16., 25.]],

        [[ 2., 11., 20.],
         [ 5., 14., 23.],
         [ 8., 17., 26.]],

        [[ 3., 12., 21.],
         [ 6., 15., 24.],
         [ 9., 18., 27.]]])
```

Answer 1

It looks like this is happening.

Suppose the tensor components are $a_{ijk}$ where $i$ tells you which matrix you're talking about, $j$ says which row you're talking about, and $k$ says which column you're talking about. The transpose you presented then has components $a_{kji}$, so transpose seems to reverse the indices, or at least swapp first/last indices.

Of course your $jk$ indices can be swapped without changing $a_{ijk}$ which means $a_{jki}$ is another possibility; you should have made the rows/columns in your choice of $a$ distinguishable so you can better see what the operation is doing.