Respuesta :
Given a matrix A of dimension (m × n), where m is the number of rows and n is the number of columns.
The transpose of matrix A is obtained by interchanging the rows and columns.
This implies that
[tex]\begin{gathered} \text{transpose of matrix A,} \\ A^T\text{ = (n }\times\text{ m)} \\ \text{where } \\ n\text{ is the number of rows} \\ m\text{ is the number of columns} \end{gathered}[/tex]For two matrices to be conformable for multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
Thus, matrix A and its transpose are conformable since the number of columns in matrix A is equal to the number of rows in its transpose.
[tex]\begin{gathered} A\times A^T \\ (m\times n)\times(n\times m) \end{gathered}[/tex]When the matrix A and its transpose are multiplied, we obtain a square and symmetric matrix.
