The transpose of a matrix A is obtained by interchanging its rows and columns and is denoted by A' or AT.
i) If A = [aij]mxn is a matrix of order mxn, the transpose of A = A' = [aji]nxm is a matrix of order nxm.
ii) (i, j)th element of A = (j, i)th element of A’.
i) (AT)T = A.
ii) (A + B)T = AT + BT, A and B being of the same order.
iii) (KA)T = KAT, k be any scalar (real or complex).
iv) (AB)T = BT AT; A and B being conformable for the product AB.
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