I am given $A = \begin{pmatrix} a & b\\ c & d \end{pmatrix} $ and B = $ \begin{pmatrix} e & f\\ g & h \end{pmatrix}$ whose elements are non-zero reals.
If $BA = I$, where $I$ is the $2 \times 2$ identity matrix and $D$ is the value of the determinant of $B$, then find the value of $D$
Assume that four options are given for the correct answer (which is $\frac{d}{e}$) and only one is correct. How can I find the correct answer quickly?
ADDED:
The answer suggested in my module is $\frac{d}{e}$, so I am suppose to derive to that point.