In the Solow growth model, does labor grow like technology at the steady state? The Solow growth model defines 

$$k_t \equiv \frac{K_t}{A_t L_t}$$

Let our production function be Cobb Douglas 

$$Y_t = K_t^\alpha (A_t L_t)^{1-\alpha}$$ 

We have 

$$A_t = A_0 e^{gt}$$
$$L_t = L_0 e^{nt}$$

We find the steady state is 

$$k^* = \left(\frac{s}{n+ g + \delta}\right)^{\frac{1}{1-\alpha}}$$

At the steady state, we notice 

$$\frac{K_t}{L_t} = A_t k_t = A_0 e^{gt}  \left(\frac{s}{n+ g + \delta}\right)^{\frac{1}{1-\alpha}}$$

My Question

Does $$\frac{K_t}{A_t} = L_t k_t = L_0 e^{nt}  \left(\frac{s}{n+ g + \delta}\right)^{\frac{1}{1-\alpha}}$$

also grow at the steady state? In several lecture notes I found online, no one discusses this so I wanted to clarify.

Follow Up 

But if $\frac{K_t}{L_t}$ and $\frac{K_t}{A_t}$ both grow this way, then 

$$K_t = A_0 e^{gt} L_0 e^{nt}  \left(\frac{s}{n+ g + \delta}\right)^{\frac{1}{1-\alpha}}$$

So does this mean $K_t$ is a function of these parameters (e.g. $A_0$) or is this not a valid economic expression?
In deterministic growth models of closed economies with exogenous constant growth drivers (here, population and labor efficiency), the steady-state of the economy is in "growth rates", or under the newer terminology, it is a "balanced growth path".  

The growth rate of the economy can only be the sum of the growth rates of these exogenous growth drivers. So in the balanced growth path, aggregate magnitudes grow at $n+g$, per capita magnitudes grow at $g$ and magnitudes per efficiency unit of labor are constant.  

One can see this directly through the production function by considering

$$Y_t = K_t^\alpha (A_t L_t)^{1-\alpha} \implies \ln Y = \alpha \ln K_t + (1-\alpha)\cdot [\ln A_t + \ln L_t]$$

$$\implies \frac {\text{d}\ln Y}{\text{d}t} = \frac {\dot Y}{Y} = \alpha \frac {\dot K}{K} + (1-\alpha)\cdot \left[\frac {\dot A}{A} + \frac {\dot L}{L}\right]$$

$$\implies \frac {\text{d}\ln Y}{\text{d}t} = \frac {\dot Y}{Y} = \alpha \frac {\dot K}{K} + (1-\alpha)\cdot (g+n)$$

To have a balanced growth path, we must have equal and constant growth rates (so ratios like $Y/K$ etc remain constant), therefore

$$\frac {\dot Y}{Y} = \frac {\dot K}{K} = \gamma$$

$$\implies \gamma = \alpha \gamma + (1-\alpha)\cdot (g+n)$$

$$\implies \gamma = g+n$$

Note the importance of constant returns to scale, in order to obtain this result.