3x3

4x4

5x5

6x6

7x7

8x8

*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 \(b_{ij}=a_{ji}\)

a) \((A + B)^T = (A + B)^T\);

b) \((A^T)^T = A\);

c) \((kA)^T = kA^T\);

d) \((AB)^T = A^T B^T\);.