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 = InA

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

In = 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

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