Diagonalization & Matrix Powers · Challenge problem

A planar fluid flow has velocity field $\mathbf v = A\mathbf x$ with $A = \begin{pmatrix}4 & 1\\-2 & 1\end{pmatrix}$. Diagonalizing $A$ shows that $\det(e^{At}) = e^{(\operatorname{tr}A)t}$, so a small blob of area $1$ at $t=0$ has area $e^{(\operatorname{tr}A)t}$ at time $t$. Find the time at which the blob's area has TRIPLED.