Transpose of a Matrix

• The transpose of a matrix is obtained by flipping the rows and columns of the original matrix.
• The dimensions of the transpose matrix are opposite to that of the original matrix.
• The transpose of a transpose matrix is equal to the original matrix.
• Transposition is a linear operation, meaning that (A+B)^T = A^T + B^T and (kA)^T = k(A^T), where A and B are matrices and k is a scalar.
• The transpose of a product of matrices is equal to the product of their transposes in reverse order, i.e., (AB)^T = B^T A^T.
  

 Important Formula in this topic

Transpose of a Matrix: $$A^T = [a_{ji}]$$