The mutual inductance $\mathbf{M}_{12}$ of coil increases when they are brought nearer and is the same as $\mathrm{M}_{12}$ of coil 2 with respect to coil 1.
$\left(\mathrm{M}_{21}\right)$, mutual inductance of solenoid $\mathrm{S}_1$ with respect to solenoid $\mathrm{S}_2$
$$
\mathrm{M}_{21}=\mu_0 \mathrm{n}_1 \mathrm{n}_2 \pi \mathrm{r}_1^2 l
$$
where $\mathrm{r}_1 l$ is the common area of cross-section of coil and common length ( $l$ ) so $\mathrm{M}_{12}$ on passing current and rotation.


So, $\mathrm{M}_{12}$ i.e., mutual inductance of solenoid $\mathrm{S}_2$ with respect to solenoid $\mathrm{S}_1$ is
$$
\mathrm{M}_{12}=\mu_0 \mathrm{n}_1 \mathrm{n}_2 \pi \mathrm{r}_1^2 l
$$
So, we get, $\quad M_{12}=M_{21}=M$