Transpose Of Matrix

Transpose of Matrix:

If A = [ a_ij ] is an m n matrix, then the transpose of  A is A^T = [ a_ij ] which is an n m matrix. Thus the transpose of A is obtained from A by interchanging the rows and column of A. We obtain

Example-8:

Properties of transpose:

Let S be a scalar and A and B be the matrices. Then

1. ( AT)^T = A

2. ( A B )^T = A^T B^T

3. ( AB )^T = B^T A^T

4. ( sA )^T = sA^T

Example-9: