PROPERTIES OF INVERSE OF MATRICES EXAMPLE PROBLEMS

Problem 1 :

Solution :

|A|  =  (1/9) [-8(16 + 56) - 1(16 - 7) + 4(-32 - 4)]

  =  (1/9)[-8(72) - 1(9) + 4(-36)]

  =  (1/9)[-576 - 9 - 144]

  =  (1/9)(-729)

  =   -81

(1) = (2)

Problem 2 :

Solution :

|A|  =  24 - 20

|A|  =  4

(1)  =  (2)  =  (3)

Problem 3 :

Solution :

(AB)^-1  =  (1/|AB|)  adj AB

|AB|  =  -77 + 90

|AB|  =  13

(AB) ^-1  =  B^-1 A^-1

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