Chapter 10.4, Problem 29E

(a)

To determine

To show: The matrix $EA$ is the matrix $A$ with its rows permuted in exactly the same order that the rows of $I_n$ has permuted to form the matrix $E$.

(b)

To determine

To show: The matrix $A{E}^T$ is the matrix $A$ with its columns permuted in exactly the same order that the rows of $I_n$ has permuted to form the matrix $E$ by apply the result of part (a) to $A^T$.

(c)

To determine

To explain: The matrix $EA{E}^T$ is the matrix $A$ with its rows and columns permuted in exactly the same order that the rows of $I_n$ has permuted to form the matrix $E$.

(d)

To determine

To explain: Does it matter whether thee rows of the matrix or columns of the matrix are permuted first to find the canonical form of the transition matrix.