The dimension $[MLT^{-2}A^{-2}]$ belong to the :

Magnetic permeability: from $B = \frac{\mu_0 I}{2\pi r}$, $\mu_0 = \frac{2\pi r B}{I}$ $[B] = [MT^{-2}A^{-1}]$, so $[\mu_0] = \frac{[L][MT^{-2}A^{-1}]}{[A]} = [MLT^{-2}A^{-2}]$ So $[MLT^{-2}A^{-2}]$ belongs to magnetic permeability.