If A is a skew-symmetric matrix and $n\in N$ such that $(A^n)^T=\lambda A^n, \lambda $ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $(-1)^n$
If A is a skew-symmetric matrix,
$A^T=-A$
$⇒(A^n)^T=(A^T)^n$
$=(-A)^n=(-1)^nA^n$
$⇒λ=(-1)^n$