Question:medium
If \(a\) is a real root of the equation
\[
x^{3}-2x^{2}-2x-3=0
\]
and
\[
A=
\begin{bmatrix}
1& 2& a\\
2& a& 1\\
a& 1& 2
\end{bmatrix},
\]
then \(A^{2}-A=\)
If \(a\) is a real root of the equation
\[
x^{3}-2x^{2}-2x-3=0
\]
and
\[
A=
\begin{bmatrix}
1& 2& a\\
2& a& 1\\
a& 1& 2
\end{bmatrix},
\]
then \(A^{2}-A=\)
Show Hint
Whenever a parameter inside a matrix satisfies an algebraic equation, determine the parameter first. Matrix calculations become much simpler afterward.
Updated On: Jun 22, 2026
Show Solution
The Correct Option is C
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