MHT CET2007MathematicsMatrices
If A is a square matrix of order n n , then adj ( adj A) is equal to
Options
- A| .A |^ n A
- B|A|^ n-1 A
- C|A|^ n-2 A
- D|A|^ n-3 A
Correct answer
C. |A|^ n-2 A
Step-by-step solution
For any square matrix B , we have B( adj B)=|B| I_ n On taking B= adj A , we get ( adj A)[ adj ( adj A)]=| adj A| I_ n adj A[ adj ( adj A)]=|A|^ n-1 I_ n ( | adj A|=|A|^ n-1 ) (A adj A)[ adj ( adj A)]=|A|^ n-1 A (|A| I_ n )[ adj ( adj A)]=|A|^ n-1 A ( adj A)=|A|^ n-2 A