Have you worked out $\displaystyle A^2$? This is normally the first thing you would try in any problem such as this. For this one, if you calculate $\displaystyle A^2$, you’ll find it’s quite a nice, helpful matrix.
$\displaystyle A^2=I$, the identity matrix, so $\displaystyle A^{74}=I$ as well because that will be the identity matrix multiplied by itself 37 times. $\displaystyle A^{75} = A^{74}A = A$. Yes, it is equal to itself.