Definition: The transpose of a matrix \(A\), written \(A^T\), is the matrix obtained by writing the columns of A, in order, as rows. That is, if \(A=[a_{ij}]\) is an \(m \times n\) matrix, then \(A^T=[b_{ji}]\) is the \(n \times m\) matrix where \(b_{ij}=a_{ji}\)
Few theorems that may facilitate calculations of matrix transpose: a) \((A + B)^T = (A + B)^T\); b) \((A^T)^T = A\); c) \((kA)^T = kA^T\); d) \((AB)^T = A^T B^T\);.