How to solve this problem

Let o : {1,...,n} - {1, ...,n} be a bijection. (We call such a bijection a permutation. ) Define T : Fn - F" by [T(x)]; = No(i). Show that T is a linear transformation, and compute its standard matrix, which we shall denote P. (Such a matrix is called a permutation matrix. ) Show that for A E Foxm and BE Fmx, the i-th row of PA is the o(i)-th row of A, and the j-th column of BP is the o (j)-th column of B