Why use two affine transformations in Multivariate Cryptography? I'm reading Multivariate Cryptography and would like to know why we use two affine transformations to scramble the central map?

Why not use only one?
In the majority of multivariate cryptographic schemes (MQ) the encryption/signature function $E$ is a composition of secret affine invertible transformations $A,B$ and a nonlinear transformation $P$ (can be secret or public):
$$
E = B\circ P\circ A
$$

$P$ is typically invertible, and the goal of the scheme is to make $E$ non-invertible even though it is fully exposed to an attacker as a polynomial.

The mere fact that $P$ is invertible explains why we need both $A$ and $B$. Indeed, suppose that $A$ is missing, then in the equation
$$
E(x) = B(P(x))
$$
we substitute 
$$
x = P^{-1}(y)
$$
and obtain
$$
E(P^{-1}(y)) = B(y),
$$
so we know $B$ and are able to invert $B$.

This is the simplest case; there are other variants, where $P$ is secret, or its inverse is not available in the closed form, or some of the output polynomials are dropped (OK for signatures). In some of these variants both $A$ and $B$ are still required as otherwise you could invert the scheme just by looking at the structure of the polynomial and comparing monomials of $E$ with monomials of $P$. However, say, if $P$ is secret, then both $A$ and $B$ can be considered as part of $P$.