Properties of Transpose Matrix

Theorem

If the sizes of the matrices are such that the stated operations can be performed, then

1. $(A^T{)}^T=A$
2. $(A\pm B{)}^T=A^T\pm B^T$
3. $(kA{)}^T=k{A}^T$
4. $(AB{)}^T=B^T{A}^T$
5. $(A_1{A}_2\dots A_n{)}^T=A_n^T\dots A_2^T{A}_1^T$