  Let $G$ be a cancellative $3$-uniform hypergraph in which the symmetric
difference of any two edges is not contained in a third one. Equivalently, a
$3$-uniform hypergraph $G$ is cancellative if and only if $G$ is $\{F_4,
F_5\}$-free, where $F_4 = \{abc, abd, bcd\}$ and $F_5 = \{abc, abd, cde\}$. A
classical result in extremal combinatorics stated that the maximum size of a
cancellative hypergraph is achieved by the balanced complete tripartite
$3$-uniform hypergraph, which was firstly proved by Bollob\'as and later by
Keevash and Mubayi. In this paper, we consider spectral extremal problems for
cancellative hypergraphs. More precisely, we determine the maximum $p$-spectral
radius of cancellative $3$-uniform hypergraphs, and characterize the extremal
hypergraph. As a by-product, we give an alternative proof of Bollob\'as' result
from spectral viewpoint.
