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If $A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(i)\quad(A')'=A$

Note: This is part 1 of a 3 part question, split as 3 separate questions here.

1 Answer

Toolbox:
  • If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
Given:-
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}$
$A'=\begin{bmatrix}0 & 4\\-1 & 3\\2 & -4\end{bmatrix}$
Transpose of a matrix is obtained by changing the rows into column.
$(A')'=\begin{bmatrix}0 &4\\-1 & 3\\2 & -4\end{bmatrix}$
$\;\;\;\;\;\;=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}$
$\;\;\;\;\;\;=A.$
$\Rightarrow (A')'=A.$
answered Mar 19, 2013 by sharmaaparna1
 

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