  Within the field of multilinear algebra, inverses and generalized inverses of
tensors based on the Einstein product have been investigated over the past few
years. In this paper, we explore the singular value decomposition and full-rank
decomposition of arbitrary-order tensors using {\it reshape} operation.
Applying range and null space of tensors along with the reshape operation; we
further study the Moore-Penrose inverse of tensors and their cancellation
properties via the Einstein product. Then we discuss weighted Moore-Penrose
inverses of arbitrary-order tensors using such product. Following a specific
algebraic approach, a few characterizations and representations of these
inverses are explored. In addition to this, we obtain a few necessary and
sufficient conditions for the reverse-order law to hold for weighted
Moore-Penrose inverses of arbitrary-order tensors.
