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# Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:$(e)\;(A^T)^T=A.$

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• 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$=\begin{bmatrix}1 & 2\\-1 & 3\end{bmatrix}$
$A^T$=Matrix obtained by interchanging the rows and columns is called the transpose of a matrix.
$(A^T)=\begin{bmatrix}1 & -1\\2 & 3\end{bmatrix}$
$(A^T)^T=\begin{bmatrix}1 & 2\\-1 & 3\end{bmatrix}$
Again interchange the rows and column.
$(A^T)^T=A.$
Hence LHS=RHS