# Transpose of Matrix

The matrix obtained from any given matrix

*A*, by interchanging rows and columns, is called the transpose of*A*and is denoted by*A*^{T}.If

*A*= [*a*]_{ij}_{m}_{ Ã— n}and*A*^{T}= [*b*]_{ij}_{n}_{ Ã— m}then*b*=_{ij}*a*, âˆ€_{ji}*i*,*j.*For example, if

*A*= , then*A*^{T}= .# Properties of transpose

- (
*A*^{T})^{T}=*A* - (
*A*+*B*)^{T}=*A*^{T}+*B*^{T},*A*and*B*being conformable matrices - (
*Î±A*)^{T}=*Î±A*^{T},*Î±*being scalar - (
*AB*)^{T}=*B*^{T}*A*^{T},*A*and*B*being conformable for multiplication**(reversal law)**