Matrices And Determinants

Let \(M = \left[ {\matrix{ 0 & { - \alpha } \cr \alpha & 0 \cr } } \right]\), where \(\alpha\) is a non-zero real number an \(N = \sum\limits_{k = 1}^{49} {{M^{2k}}}\). If \((I - {M^2})N = - 2I\), then the positive integral value of \(\alpha\) is ____________.