Find the inverse of each of the following matrices by using elementary row transformations:

Given:- 2 x 2 square matrix

Tip:- Algorithm to find Inverse of a square matrix of ‘n’ order by elementary row transformation

(i) Obtain the square matrix, say A

(ii) Write A = I_nA

(iii) Perform a sequence of elementary row operation successively on A on the LHS and pre-factor I_n on the RHS till we obtain the result

I_n = BA

(iv) Write A^-1 = B

Now,

We have,

A = I₂A

Where I₂ is 2 x 2 elementary matrix

⇒

Applying

⇒

Applying

⇒

Applying

⇒

Applying

⇒

Hence, it is of the form

I = BA

So, as we know that

I = A^-1A

Therefore

A^-1 = B

⇒ inverse of A