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Transpose of a Matrix

If

The matrix

In other words, the matrix of order

Now,

**A = [a**be a matrix of order_{ij}]**p × q**then the matrix**B = [b**of order_{ij}]**q × p**is called transpose of the matrix**A**if**b**_{ij}= a_{ij}for all values of**i**and**j**, i.e. the**(i, j)th**element of**B**is equal to**(j, i)th**element of**A**.The matrix

**B**is also written as**B = A’**.In other words, the matrix of order

**q × p**obtained from**A**by interchanging its rows and columns is called transpose of**A**, e.g.**Property:**The transpose of the transpose of a matrix**A**is the matrix**A**itself, i.e.**(A’)’ = A**.**Proof:**Let**A = [aij]**be a matrix of order**p × q**, then**A’ = [c**, where_{ij}]**c**_{ji}= a_{ij}for all**1 ≤ i ≤ p ; 1 ≤ j ≤ q (i)**

Now,

**(A’)’ = [d**, where_{ij}]**d**for all_{ij}= c_{ji}**1 ≤ i ≤ p ; 1 ≤ j ≤ q (ii)****(i)**And**(ii) d**_{ij}= a_{ij}, for all values of_{i}and_{j}**(A’)’ = A**.**Services: -**Transpose of a Matrix Homework | Transpose of a Matrix Homework Help | Transpose of a Matrix Homework Help Services | Live Transpose of a Matrix Homework Help | Transpose of a Matrix Homework Tutors | Online Transpose of a Matrix Homework Help | Transpose of a Matrix Tutors | Online Transpose of a Matrix Tutors | Transpose of a Matrix Homework Services | Transpose of a MatrixSubmit Your Query ???

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