Obtain the inverses of the matrices and . And, hence find the inverse of the matrix .

Let


To find: A-1, B-1 and C-1


Calculating A-1


We have,


We have to find A-1 and


Firstly, we find |A|


Expanding |A| along C1, we get




= 1(1 – 0)


= 1


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












…(i)


Calculating B-1


We have,


We have to find B-1 and


Firstly, we find |A|


Expanding |B| along C1, we get




= 1(1 – 0) – q(0)


= 1


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













…(ii)


Calculating C-1


Here,



C = AB


C-1 = (AB)-1


We know that,


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


Substitute the values, we get




Ans. , and .


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