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?