Transpose

The transpose of a matrix A is another matrix where the rows of A are written as columns. Vectors can be transposed in the same way. We can write the transpose of A using different symbols such as AT, A′ Atr and At. 
Examples.
Here is the vector formula_1 being transposed:
Here are a few matrices being transposed:
Properties.
Given two matrices A and B, the following properties related to the transpose are true: