Transpose Of Matrices


If A = [aij] be an m × n matrix, then the matrix obtained by interchanging the rows and columns of A is called the transpose of A. Transpose of the matrix A is denoted by A' or (At). In other words, if A = [aij]m × n, then A'= [aji]n × m.

eg Given the following matrix A : 


Transpose of Above matrix is given by  A' :



Properties of Matrix transpose:

1. If a matrix is transposed twice, it leads to original matric istestlf. ie if A is a matrix of mxn order, then ( ( Amxn ' ) ' ) = A mxn

2. If A is a matrix and k is a scaler quantity , then  (kA) ' = k (A'), 

3. If A and B are two different matrices, then 

  •     ( A + B ) ' = ( A' + B' )
  •     (A . B )'  = A' . B'




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