We know that one match from $G=(V,E)$ be a subset of edges $M \subset_= E $ in such a way non two edges of M hasn't a common vertex. Matches M is Maximal if M not a proper subset of any other matches of G.
a) if $M_1, M_2$ be an arbitrary matches of $G=(V,E)$, then $G' = (V, M_1 \cup M_2)$ is bipartite.
b) if $M_1, M_2$ be two maximal matches, then $|M_1| \leq 3/2 |M_2|$.
why a is true and b is false?
a) A graph is bipartite if and only if it hasn't any cycle with an odd number of nodes. If $M_1\cup M_2$ has one of them, then surely there are two edges from $M_1$ or $M_2$ with a vertex in common, that is an absurd.
b) Take the path with 4 nodes and 3 edges, connected as follow: $(1,2), (2,3), (3,4)$. Then both $\{(2,3)\}$ and $\{(1,2),(3,4)\}$ are maximal matches, but $2>3/2$.