NCERT Solutions for Class 12 Maths Chapter 3 Matrices 
                   
       
      Exercise 3.3                                                           Page No: 88 
       
      1. Find the transpose of each of the following matrices: 
                          
      Solution:  
       
                                            
      2. If A =     and B =       then verify that: 
       
                                   
      Solution:   
                                        
                                              
                                          
                                         NCERT Solutions for Class 12 Maths Chapter 3 Matrices 
                                     
              
             Again,                                
              
             Proved.                                       
              
                                                                                     
                                              
                                                          
             Hence proved. 
              
             3. If A’ =            and B =                 then verify that: 
              
                                                                                             
                     
                    NCERT Solutions for Class 12 Maths Chapter 3 Matrices 
                   
       
      (i)          
      (ii)           
       
      Solution:  
                           
      As we know that (A’)’ = A, we have 
       
                   
      LHS:                 
                   
      RHS: 
      LHS = RHS              
       
      (ii) 
      LHS                           
       
                                              
                                         
                                        NCERT Solutions for Class 12 Maths Chapter 3 Matrices 
                                    
                                     
             RHS: 
                                                            
             LHS = RHS 
              
             4. If A’ =           and B =              then find (A + 2B)’. 
              
             Solution: 
                                    
             Find A + 2 B 
             And                                   
                                    
             5. For the matrices A and B, verify that (AB)’ = B’A’, where: 
                                                 
             Solution: LHS