The dimension of mutual inductance is

e₂ : induced emf in secondary coil
i₁ : Current in primary coil
M : Mutual inductance
$\begin{array}{r}{\mathrm{e}}_2=-\mathrm{M}\frac{{\mathrm{di}}_1}{\mathrm{dt}}\\ \mathrm{M}=-\frac{{\mathrm{e}}_2}{\frac{{\mathrm{di}}_1}{\mathrm{dt}}}\end{array}$
$\left[\mathrm{M}\right]=\frac{\left[{\mathrm{e}}_2\right]}{\left[\frac{{\mathrm{di}}_1}{\mathrm{dt}}\right]}=\frac{\left[\frac{\mathrm{W}}{\mathrm{q}}\right]}{\left[\frac{{\mathrm{di}}_1}{\mathrm{dt}}\right]}=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{AT}}^{\left[{\mathrm{AT}}^{-1}\right]}\right.}$
$=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{A}}^{-2}\right]$