Matrices & Determinants · Inverse of a matrix

Let

A

B

and

C

be three

2\times2

matrices with real entries such that

B = (I + A)^{-1}

and

A + C = I

. If

BC = \begin{bmatrix} 1 & -5\\ -1 & 2\end{bmatrix} \quad\text{and}\quad CB\begin{bmatrix} x_1\\ x_2\end{bmatrix} = \begin{bmatrix} 12\\ -6\end{bmatrix},

then

x_1 + x_2

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