If A is a skew-symmetric and n ∈ N such that


If $A$ is a skew-symmetric and $n \in N$ such that $\left(A^{n}\right)^{T}=\lambda A^{n}$, write the value of $\lambda$.


Given: A is skew symmetric matrix.

$\Rightarrow A^{T}=-A$

$\left(A^{n}\right)^{T}=\lambda A^{n}$

$\Rightarrow\left(A^{T}\right)^{n}=\lambda A^{n}$

$\Rightarrow(-A)^{n}=\lambda A^{n}$

$\Rightarrow(-1)^{n} A^{n}=\lambda A^{n}$


$\Rightarrow \lambda=(-1)^{n}$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now