Let M ={ A = (a, b; c, d): a, b, c, d ∈{ ± 3, ± 2, ± 1,0}}. Define f: M → Z, as f( A )= det ( A ), for all A ∈ M, where Z is set of all integers.…

Let $\displaystyle \mathrm{M}=\left\{\mathrm{A}=\left(\begin{array}{ll}\mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{d}\end{array}\right): \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \in\{ \pm 3, \pm 2, \pm 1,0\}\right\}$. Define $\displaystyle f: \mathrm{M} \rightarrow \mathrm{Z}$, as $\displaystyle f(\mathrm{~A})=\operatorname{det}(\mathrm{A})$, for all $\displaystyle \mathrm{A} \in \mathrm{M}$, where Z is set of all integers. Then the number of $\displaystyle \mathrm{A} \in \mathrm{M}$ such that $\displaystyle f(\mathrm{~A})=15$ is equal to \_\_\_\_.