if A is a matrix...

what does A raised to T signify???

It means transpose of A.

This gives another matrix whose rows are the columns of the original matrix, and whose columns are the rows.

Simply put it is a matrix with rows and columns interchanged from the original matrix..

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A^T means transpose of A.It is obtained by interchanging rows and columns of A.It's determinant is same as that of A.

 means transpose of any matrix which is found by interchanging column and rows,it is also denoted as .