If A is a skew-symmetric and n ∈ N such that (An)T = λAn, write the value of λ.
Let A is a skew – symmetric matrix, then
AT = - A …(i)
Consider
⇒ (An)T = λAn [given]
⇒ (AT)n = λAn
⇒ (-A)n = λAn [from (i)]
⇒ (-1)n(A)n = λAn
Comparing both the sides, we get
λ = (-1)n