Answer :

Given:


To Verify: (AB)-1= B-1A-1


Firstly, we find the (AB)-1


Calculating AB





We have to find (AB)-1 and


Firstly, we find the adj AB and for that we have to find co-factors:


a11 (co – factor of 34) = (-1)1+1(94) = (-1)2(94) = 94


a12 (co – factor of 39) = (-1)1+2(82) = (-1)3(82) = -82


a21 (co – factor of 82) = (-1)2+1(39) = (-1)3(39) = -39


a22 (co – factor of 94) = (-1)2+2(34) = (-1)4(34) = 34



Now, adj AB = Transpose of co-factor Matrix



Calculating |AB|





= [34 × 94 – (82) × (39)]


= (3196 – 3198)


= -2



Now, we have to find B-1A-1


Calculating B-1


Here,


We have to find A-1 and


Firstly, we find the adj B and for that we have to find co-factors:


a11 (co – factor of 6) = (-1)1+1(9) = (-1)2(9) = 9


a12 (co – factor of 7) = (-1)1+2(8) = (-1)3(8) = -8


a21 (co – factor of 8) = (-1)2+1(7) = (-1)3(7) = -7


a22 (co – factor of 9) = (-1)2+2(6) = (-1)4(6) = 6



Now, adj B = Transpose of co-factor Matrix



Calculating |B|





= [6 × 9 – 7 × 8]


= (54 – 56)


= -2



Calculating A-1


Here,


We have to find A-1 and


Firstly, we find the adj A and for that we have to find co-factors:


a11 (co – factor of 3) = (-1)1+1(5) = (-1)2(5) = 5


a12 (co – factor of 2) = (-1)1+2(7) = (-1)3(7) = -7


a21 (co – factor of 7) = (-1)2+1(2) = (-1)3(2) = -2


a22 (co – factor of 5) = (-1)2+2(3) = (-1)4(3) = 3



Now, adj A = Transpose of co-factor Matrix



Calculating |A|





= [3 × 5 – 2 × 7]


= (15 – 14)


= 1



Calculating B-1A-1


Here,


So,





So, we get


and


(AB)-1 = B-1A-1


Hence verified


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