Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:
If $A=\begin{bmatrix} 3 & -2\\ 4 & -2\\ \end{bmatrix}$ and $ I=\begin{bmatrix} 1 & 0\\ 0 & 1\\ \end{bmatrix}$, then for what value of $k$ we have $A^2=kA-2I$
Options:
$k=1$
$k=2$
$k=-1$
$k=3$
Correct Answer:
$k=-1$
Explanation:
Solving the matrix equation $A^2-kA+2I=0$ will give the values of $k$.