A ring R is said to have stable range one if for any \(a,x\in R\) , there exists a \(t\in R\) such that \(a+(1-ax)t=u\) is a unit of R. A nonsingular matrix \(S_W(X,Y)\) is constructed over such ring. Consequently for any \(A\in \mathbb {C}^{n\times n}\) , \(X\in A\{2\}\) , it is proved that for any matrix \(B,C^*\) with full column rank satisfying \(R(B)=N(X)\) and \(N(C)=R(X)\) , \(\left( {\begin{matrix} A & B \\ C & 0 \end{matrix}}\right) ^{-1}=\left( {\begin{matrix} X & & GB(CB)^{-1}\\ (CB)^{-1}C& & -(CB)^{-1}CAB(CB)^{-1} \end{matrix}}\right) \) for some matrix G if and only if \(AX=XA^2X\) and there is a nonsingular matrix W such that \(AXW=AXA\) and \(W(I_n-XA)=UQ_WY\) for some nonsingular matrix \(Q_W\) , where \(I_n-AX=UY\) is a full rank factorization. And G could be any solution of the equation \(G(I_n-AX)=(I_n-XA)\) . For \(X\in \{A_d, A^{\tiny \textcircled {\tiny \dag }}, A^{ow}\}\) , A and X satisfy this equivalent condition. Besides, \(\left( {\begin{matrix} A & U\\ Y& 0 \end{matrix}}\right) ^{-1}=\left( {\begin{matrix} X & GU\\ Y& -YAU \end{matrix}}\right) .\)
