Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof resit / 5 / a / iii

True. A square matrix with matrix rank $n$ is invertible, and its transpose has the same rank. Applying the rank-nullity theorem to both $A$ and $A^T$ gives nullity zero in each case, so both kernels are $\{0\}$.