हमें पता है
\(\mathrm{A}^{2}=\mathrm{A} \cdot \mathrm{A}\)
\(=\left[\begin{array}{cc}
1 & 0 \\
-1 & 7
\end{array}\right]\left[\begin{array}{cc}
1 & 0 \\
-1 & 7
\end{array}\right]\)
\(=\left[\begin{array}{cc}
1+0 & 0+0 \\
-1-7 & 0+49
\end{array}\right]\)
\(=\left[\begin{array}{cc}
1 & 0 \\
-8 & 49
\end{array}\right] \)
\(\therefore\) \(A^2 - 8A\)
\(=\left[\begin{array}{cc}
1 & 0 \\
-8 & 49
\end{array}\right]-8\left[\begin{array}{cc}
1 & 0 \\
-1 & 7
\end{array}\right]\)
\(=\left[\begin{array}{cc}
1 & 0 \\
-8 & 49
\end{array}\right]+\left[\begin{array}{cc}
-8 & 0 \\
8 & -56
\end{array}\right] \)
\(=\left[\begin{array}{cc}
1-8 & 0+0 \\
-8+8 & 49-56
\end{array}\right]\)
\(=\left[\begin{array}{cc}
-7 & 0 \\
0 & -7
\end{array}\right]\)
\(=-7\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]\)
\(=-7 \mathrm{I}\)
इस प्रकार तुलना करने पर k = -7
