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  4. if A = [0&-1&2 1&0&3 -2&-3&0], then A + 2AT equals

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Q. if $A = \begin{bmatrix}0&-1&2\\ 1&0&3\\ -2&-3&0\end{bmatrix}$, then $ A + 2A^{T}$ equals

Matrices

Solution:

$A^{T}=\begin{bmatrix}0&1&-2\\ -1&0&-3\\ 2&3&0\end{bmatrix}= - \begin{bmatrix}0&-1&2\\ 1&0&3\\ -2&-3&0\end{bmatrix}= - A $
so, $A^{T} = -A \Rightarrow A = -A^{T}$
Hence$ A + 2A^{T }= -A^{T}+ 2A^{T}= A^{T}$