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Orthogonal Matrix

The character...

Question

The characteristic of an orthogonal matrix $A$ is

A^{- 1} . A = I

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A . A^{- 1} = I

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A^{T} . A^{- 1} = I

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A . A^{T} = I

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Solution

The correct option is C $A . A^{T} = I$
By property of orthogonal matrix
$A A^{T} = A^{T} A = I$

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Similar questions

A - \frac{1}{2} I

A + \frac{1}{2} I

∣ ∣ ∣ ∣ \begin{matrix} 1 + i & 1 - i & i 1 + i & i & 1 + i i & 1 + i & 1 - i \end{matrix} ∣ ∣ ∣ ∣

A - \frac{1}{2} I

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Matrix A is such that $A^{2} = 2 A - I,$ where I is the Identity matrix. Then for $n \geq 2, A^{n}$ is equal to

λ

λ

λ

λ

=

λ

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & 1 2 & 3 & 4 - 1 & - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦

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