Hey guys, I've been having trouble with this matrix problem for a while now.

Here it is:

M = $\displaystyle \left[ \begin{array}{cc} 7 & -3 \\ 15 & -7 \end{array} \right]$

Find all 2 x 2 matrices A = $\displaystyle \left[ \begin{array}{cc} a & b \\ b & d \end{array} \right]$ where (1,2) = (2,1) entry such that AM = -MA

I've tried matrix multiplication for both AM and -MA and tried equating appropriate values but I end up with a zero matrix. I also tried multiplying both sides by A inverse, but again I get a zero matrix. Any help is appreciated, thanks.