If A is a square matrix of order 3 - then -A-A T 2019-A- 1B- 2019C- 0D- None of these

The correct option is C 0 nbsp;(A A^T)^T=A^T (A^T)^T= (A A^T) ⇒ A A^T is skew symmetric matrix nbsp; ⇒ (A A^T)^2019 is skew symmetric matrix of order 3. ⇒ ...

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Standard XII

Mathematics

Scalar Matrix

If A is a squ...

Question

If $A$ is a square matrix of order $3$ , then $| (A - A^{T})^{2019} | =$

1

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2019

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0

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None of these

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Solution

The correct option is C $0$
$(A - A^{T})^{T} = A^{T} - (A^{T})^{T} = - (A - A^{T})$
$\Rightarrow A - A^{T} is skew-symmetric matrix \Rightarrow (A - A^{T})^{2019} is skew-symmetric matrix of order 3. \Rightarrow | (A - A^{T})^{2019} | = 0$

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If A is a square matrix of order 3, then |(A−AT)2019|=

The correct option is C 0 (A−AT)T=AT−(AT)T=−(A−AT) ⇒A−AT is skew-symmetric matrix⇒(A−AT)2019 is skew-symmetric matrix of order 3.⇒|(A−AT)2019|=0

If $A$ is a square matrix of order $3$ , then $| (A - A^{T})^{2019} | =$

The correct option is C $0$
$(A - A^{T})^{T} = A^{T} - (A^{T})^{T} = - (A - A^{T})$
$\Rightarrow A - A^{T} is skew-symmetric matrix \Rightarrow (A - A^{T})^{2019} is skew-symmetric matrix of order 3. \Rightarrow | (A - A^{T})^{2019} | = 0$