Matrices	and	Determinants	-	Class	XII
                                                   Past	Year	JEE	Questions
                                                         Questions
                   Quetion:	01
                                                1  2
                                            A.
                   Let	A	be	a	matrix	such	that	      	is	a	scalar	matrix	and	|3A|	=	108.	
                                              [     ]
                                                0  3
                         2
                   Then	A 	equals	:
                      4   −32
                   A.	
                     [       ]
                      0   36
                       36   0
                   B.	
                     [       ]
                      −32   4
                        4   0
                   C.	
                     [        ]
                      −32   36
                       36  −32
                   D.	
                     [         ]
                       0    4
                                                          Solutions
                   Solution:	01
                                                         Explanation
                   According	to	questions,	
                      1   2     λ  0
                   A.	      	=	
                     [     ]  [     ]
                      0   3     0  λ
                                       −1
                                  1  2
                          λ  0
                   ⇒	A	=	       	
                         [    ] [     ]
                          0  λ    0  3
                           λ   0   3  −2
                         1
                   ⇒	A	=	        	
                         3
                          [     ] [      ]
                           0   λ   0   1
                                       2
                                  1  −
                          λ  0
                                       3
                   ⇒	A	=	       	
                                      1
                         [    ]
                          0  λ  [0      ]
                                      3
                               2
                          λ   − λ
                               3
                   ⇒	A	=	
                               λ
                         [0      ]
                               3
                   As	|3A|	=	108
                           ∣       ∣
                            3λ  −2λ
                           ∣       ∣
                   ⇒	108	=	         	
                            0    λ
                           ∣       ∣
                       2
                   ⇒	3λ 	=	108
                      2
                   ⇒	λ 	=	36
                   ⇒	λ	=	±6
                   When	λ	=	+6
                            6   −4
                   then	A	=	
                           [      ]
                            0   2
                           36  −32
                      2
                   ⇒	A 	=	
                          [        ]
                            0   4
                   For	λ	=	-6
                       −6    4
                   A	=	
                      [        ]
                        0   −2
                           36  −32
                      2
                   ⇒	A 	=	
                          [        ]
                            0   4