Transpose of a Matrix and its properties - Linear Algebra

In this video we will learn what is a matrix transpose and its properties.
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A' or AT (among other notations).

A square matrix whose transpose is equal to itself is called a symmetric matrix;
Some properties of transpose:
The operation of taking the transpose is an involution (self-inverse).
The transpose respects addition and subtraction.