# Matrix Transpose Calculator

2x2
3x3
4x4
5x5
6x6
7x7
8x8

### Basic Information

Definition: The transpose of a matrix $$A$$, written $$A^T$$, is the matrix obtained by writing the columns of A, in order, as rows. That is, if $$A=[a_{ij}]$$ is an $$m \times n$$ matrix, then $$A^T=[b_{ji}]$$ is the $$n \times m$$ matrix where $$b_{ij}=a_{ji}$$

Few theorems that may facilitate calculations of matrix transpose:
a) $$(A + B)^T = (A + B)^T$$;
b) $$(A^T)^T = A$$;
c) $$(kA)^T = kA^T$$;
d) $$(AB)^T = A^T B^T$$;.