  In this paper, we study the reversibility of Riemann curvature and Ricci
curvature for the Matsumoto metric and prove three global results. First, we
prove that a Matsumoto metric is R-reversible if and only if it is R-quadratic.
Then we show that a Matsumoto metric is Ricci-reversible if and only if it is
Ricci-quadratic. Finally, we prove that every weakly Einstein Matsumoto metric
is Ricci-reversible.
