If you haven’t already done so, enter the commands in the example above to generate the permutation matrix E defined in (2) (you can suppress this matrix). Generate a 5 × 5 matrix A with integer entries using the command A = floor(10*rand(5))

(a) Compute the product EA and compare the answer with the matrix A. How are the two matrices related? Describe the effect on A of left multiplication by the permutation matrix E. Be specific! Compute the product AE and compare the answer with the matrix A. How are the two matrices related? Describe the effect on A of right multiplication by the permutation matrix E. Be specific!

(b) Compute E−1 and ET (recall that ET is computed in MATLAB with the command E’), and observe that they are also permutation matrices. What else do you observe about E−1 and ET ?