Q. 105.0( 3 Votes )

# Find the inverse

Answer :

Given:- 3 x 3 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_{n}A

(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 = I_{3}A

Where I_{3} is 3 x 3 elementary matrix

⇒

Applying

⇒

Applying

⇒

Applying and

⇒

Applying

⇒

Applying and

⇒

Hence , it is of the form

I = BA

So, as we know that

I = A^{-1}A

Therefore

A^{-1} = B

⇒ inverse of A

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