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 = 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 = I3A
Where I3 is 3 x 3 elementary matrix
Hence , it is of the form
I = BA
So, as we know that
I = A-1A
Therefore
A-1 = B