If $|A| = |kA|$, where $A$ is a square matrix of order 2, then sum of all possible values of $k$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $0$ ##
$|A| = |kA|$
$|A| = k^n |A|$ where $n$ is the order of matrix.
$1 = k^n$
$k^2 = 1$
$⇒k = \pm 1$
Sum of all values of $k = +1 - 1 = 0$