Matrices & Determinants · Adjoint and determinant properties

Let

A = \begin{bmatrix} 1 & 2\\ 1 & \alpha\end{bmatrix}

and

B = \begin{bmatrix} 3 & 3\\ \beta & 2\end{bmatrix}

. If

A^2 - 4A + I = O

and

B^2 - 5B - 6I = O

, then among the two statements:

(S1): $[(B - A)(B + A)]^{T} = \begin{bmatrix} 13 & 15\\ 7 & 10\end{bmatrix}$

and

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