1.4.4 Matrix transformations

Condition: Find the eigenvalues ​​and eigenvectors of the matrix \(A\). Write the matrix \( T \) reducing the matrix \( A \) to diagonal form. Find the matrix product \( T^{-1} A T \). \[ A=\left(\begin{array}{lll} 1 & 1 & 0 \\ 1 & 1 & 1 \\ 0 & 8 & 1 \end{array}\right) \]