The dimensional formula for magnetic permeability ;$\mu$ is

Magnetic permeability is a constant of proportionality that exists between magnetic induction and magnetic field intensity.

In SI units, permeability is measured in henries per meter $H/m$ or $H m^{-1}$.

Henry has the dimensions of $[ML^2T^{-2}A^{-2}]$.

Dimensions for magnetic permeability will be $[ML^2T^{-2}A^{-2}]/[L]=$$[MLT^{-2}A^{-2}]$