Lecture on Transpose
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Transpose of a matrix is a matrix formed by interchanging rows and columns.

\( A= \begin{bmatrix}a&b&c\\d&e&f\end{bmatrix} \) then \( A'= \begin{bmatrix}a&d\\b&e\\c&f\end{bmatrix} \)

Properties of transpose are:

  1. \((A')'=A\)
  2. \((A+B)'=A'+B'
    \)
  3. \(k(A')=(kA)'
    \)
  4. \((AB)'=B'A'\)
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