Limit of product of matrices with spectral radius less than 1

Question

If spectral radius of a square matrix $A$ is less than 1, then we know that $$\lim_{k \to \infty} A^k = 0.$$

Now, I want to know whether we can also conclude the following results? $$\lim_{k \to \infty} A^k (A^{T})^k = 0$$ where $A^{T}$ is the transpose of matrix $A$.

Answer 1

Hint: $A^T$ has the same eigenvalues as $A$. Then use algebraic limit rules.