9. For real numbers $a, b$, define the operation * as follows: $a * b=\left\{\begin{array}{ll}a^{2} b, & \text { when } a \geqslant b \text {; } \\ a b^{2}, & \text { when } a<b \text { . }\end{array}\right.$ Given that $3 * m=36$. Then the real number $m$ equals ( )
(A) $2 \sqrt{3}$
(B) 4
(C) $\pm 2 \sqrt{3}$
(D) 4 or $\pm 2 \sqrt{3}$
9. A.

When $3 \geqslant m$, $3 * m=9 m=36$, then $m=4$, which contradicts $3 \geqslant m$, so we discard it.
When $3 < m$, $3 * m=9 m=36$, hence $m=2 \sqrt{3}$.