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 .