Basic Manipulations
MatrixForm[a]
MatrixForm[Transpose[a]]
You can extract portions of matrices. The following give the a13 entry, the third row, and the second column of a matrix, respectively. Each row of a matrix is a row vector, each column of a matrix is a column vector.
a[[1,3]]
b[[1,3]]
a[[3]]
Transpose[a] [[2]]
Transpose[b] [[2]]