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182                                                                                 Determinants






















                            Figure 8.6: “The determinant of a product is the product of determinants.”



                            Which implies that det(MN) = 0 = det M det N.
                               Thus we have shown that for any matrices M and N,


                                                      det(MN) = det M det N

                            This result is extremely important; do not forget it!



                                                       Alternative proof






                                                        Reading homework: problem 4



                            8.3     Review Problems

                                                Reading Problems           1    , 2    , 3   , 4
                            Webwork:            2 × 2 Determinant                      7
                                          Determinants and invertibility          8, 9, 10, 11

                               1. Let
                                                                             
                                                                 m 1  m 1  m 1
                                                                   1    2    3
                                                                             2
                                                         M = m    2  m 2  m  .
                                                                              
                                                               
                                                                   1    2    3
                                                                 m 3 1  m 3 2  m 3 3
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