Find adjoint of each of the matrices in Exercises 1 and 2.
 
 
Verify A (adj A) = (adj A) A = A I in Exercises 3 and 4
 
 
Find the inverse of each of the matrices (if it exists) given in Exercises 5 to 11.
 
 
 
 
 
 

 
Verify that (AB)^{–1} = B^{–1} A^{–1}  
show that A^{2} – 5A + 7I = O. Hence find A^{–1}  
14. For the matrix find the numbers a and b such that A^{2} + aA + bI = O  
15. For the matrix Show that A^{3}– 6A^{2} + 5A + 11 I = O. Hence, find A^{–1}  
 
17. Let A be a nonsingular square matrix of order 3 × 3. Then adj A is equal to (A) A (B) A^{2} (C) A^{3} (D) 3A  
18. If A is an invertible matrix of order 2, then det (A^{–1}) is equal to (A) det (A) (B)1/det (A) (C) 1 (D) 0  