From the output of print, it is function. But according to the official document:
An Operation is a node in a TensorFlow Graph that takes zero or more Tensor objects as input, and produces zero or more Tensor objects as output. Objects of type Operation are created by calling a Python op constructor (such as tf.matmul) or tf.Graph.create_op.
it is a constructor. So I think it is a class name. But, printing the return value of tf.matmul shows it is a tensor, not an "Object of type Operation". Is the class Tensor inherited from the class Operation? I tried to find the definition of tf.matmul in tensorflow source code but could not get it.
tf.matmul (or tf.linalg.matmul) is a function. You can find its definition in the math_ops module. The behavior of these functions do depend on whether you are using eager execution (default in 2.x) or graph mode (default in 1.x).
With eager execution, the function receives a couple of eager tensors (tensors with their actual value, as opposed to "symbolic") and runs the computation of their matrix product. What you get is another eager tensor containing the result.
In graph mode, the function does not run any computation. It just receives two symbolic tensors (for which the value will not be determined until later), adds a matrix production operation to the current graph and gives you the symbolic tensor of its result. Tensors do not inherit from operations in any case. The graph contains nodes which are operations, which generally have inputs and/or outputs that are tensors. In graph mode, functions like tf.linalg.matmul usually give you the resulting tensor, not the operation, because it is more convenient (you rarely need to access the operation itself). When you give a name to these functions (e.g. name='MyMatMul'), it will be the name of the operation, and the output tensors of the operation (which in most cases is only one) will have that name plus : and its output index (e.g. MyMatMul:0). When you have a tensor t, you can access the operation that produced it with t.op. When you have an operation op, you can access the input and output tensors of the operation with op.inputs and op.outputs, and its type (the kind of operation it is representing, like MatMul) with op.type. These properties cannot be accessed with eager execution, as they only make sense when you have a graph.