I am attempting to factor the following matrix:
\begin{bmatrix} \alpha_1(1-b)-1 & \alpha_2(1-b) & \alpha_3(1-b) \\ \alpha_1(1-b) & \alpha_2(1-b)-1 & \alpha_3(1-b) \\ \alpha_1(1-b) & \alpha_2(1-b) & \alpha_3(1-b)-1 \end{bmatrix}
It is obvious that the common factor is $(1 - b)$; however, I am not sure how to deal with the values in the diagonal or even if it is at all possible to factor the matrix.
I appreciate your help.
You can factor this as $(1-b)A-I$ with $A$ the matrix of alphas and $I$ the identity matrix.