If velocity [V] time [T] and force [F] are chosen as the base...

$[ M{]}^{1} = [ V{]}^{a} [ T{]}^{b} [ F{]}^{c}$
$[ M{]}^{1} = {\left[L{T}^{- 1}\right]}^{a} [ T{]}^{b}{\left[ML{T}^{- 2}\right]}^{c}$
$[ M{]}^{1} = [ M{]}^{c} [ L{]}^{a + c} [ T{]}^{- a + b - 2c}$
Thus,

$\begin{cases}c = 1, & a + c = 0\text{and} & b - a - 2c = 0 \\ ⇒ a = - 1 & ⇒ b = - 1 + 2 = 1\end{cases}$
Thus, $[ M ] = [ V{]}^{- 1} [ T{]}^{1} [ F{]}^{1}$