If A is a skew symmetric matrix such that A T A - I- then A 4 n -1- n - N is equal toA- IB- -IC- AT D- - A T

The correct option is C A^T Given, A is skew symmetric matrix So, A^T= A Also A^TA = I ⇒ A^2=I Taking square of both sides, we get A^4 = I ⇒ A^4n=I ⇒ A^4n 1= ...

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Standard XII

Mathematics

Orthogonal Matrix

If A is a ske...

Question

If $A$ is a skew symmetric matrix such that $A^{T} A = I$ , then $A^{4 n - 1}, (n ϵ N)$ is equal to

$- A^{T}$

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$I$

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$- I$

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$A^{T}$

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Solution

The correct option is D
$A^{T}$

Given, $A$ is skew symmetric matrix

So, $A^{T} = - A$

Also $A^{T} A = I \Rightarrow - A^{2} = I$
Taking square of both sides, we get $A^{4} = I$

$\Rightarrow A^{4 n} = I$

$\Rightarrow A^{4 n - 1} = A^{4 n} A^{- 1} = I A^{- 1} = - A = A^{T}$

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If A is a skew symmetric matrix such that ATA=I, then A4n–1, (nϵN) is equal to

The correct option is D AT Given, A is skew symmetric matrix So, AT=−A Also ATA=I⇒−A2=I Taking square of both sides, we get A4=I ⇒A4n=I ⇒A4n−1=A4nA−1=IA−1=−A=AT

If $A$ is a skew symmetric matrix such that $A^{T} A = I$ , then $A^{4 n - 1}, (n ϵ N)$ is equal to

The correct option is D
$A^{T}$

Given, $A$ is skew symmetric matrix

So, $A^{T} = - A$

Also $A^{T} A = I \Rightarrow - A^{2} = I$
Taking square of both sides, we get $A^{4} = I$

$\Rightarrow A^{4 n} = I$

$\Rightarrow A^{4 n - 1} = A^{4 n} A^{- 1} = I A^{- 1} = - A = A^{T}$