**Transpose of a Matrix**

Let A be a matrix. Then a new matrix
obtained by interchanging the corresponding rows and columns of A is called the
**transpose** of A. It is denoted by A’
or A^{t}.

Here, the order of matrix A is 2 × 3 and that of A^{t} is 3 × 2. Hence if the
order of a matrix A is m × n, then the order of transpose of matrix A i.e. A^{t} will be n × m. If A is a
square matrix of order n, then its transpose A^{t} is also a square matrix of
order n. If A is a row matrix, then its transpose A^{t} is a column matrix.

For example:

**Properties of Transpose of a Matrix**

**1. ****The transpose of the
transpose of a matrix is the matrix itself, i.e. (A ^{t})^{t} =
A.**

**2. ****The transpose of the sum
of two matrices is equal to the sum of their transposes, i.e. (A + B) ^{t}
= A^{t} + B^{t}.**

**3. ****If A is any matrix and k
is any number, then (kA) ^{t} = kA^{t}.**

**4. ****If A and B are two
matrices conformable for multiplication, then (AB) ^{t} = B^{t}A^{t}.**

*Worked Out Examples*

*Worked Out Examples*

*You can comment your questions or problems regarding the
transpose of matrices and their properties here.*

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