Thread: How to find inverse matrix of a 3*3 or of having order > 3 in a easy way

I know finding inverse of a matrix in 3 ways 1) if 2*2 1/(ad-bc)[d -b] [-c a] 2) if order is >3 by elementary row operations with identity matrix [ -1 2 -3 | 1 0 0 ] [ 2 1 0 | 0 1 0 ] [ 4 -2 5 | 0 0 1 ] like dis on reducing into In ; B 3) through eigen value process sir all of dese processes are taking bulk of time in xams. I request you to tell me if u r known with any other easiest way

Originally Posted by achasiri

I know finding inverse of a matrix in 3 ways 1) if 2*2 1/(ad-bc)[d -b] [-c a] 2) if order is >3 by elementary row operations with identity matrix [ -1 2 -3 | 1 0 0 ] [ 2 1 0 | 0 1 0 ] [ 4 -2 5 | 0 0 1 ] like dis on reducing into In ; B 3) through eigen value process sir all of dese processes are taking bulk of time in xams. I request you to tell me if u r known with any other easiest way

Write out your post properly, pressing the `return' key every once in a while and spelling `these' correctly, and then I will tell you my thoughts on the matter (your post is pretty much illegible the way it is).

Also, to get the matrix to be displayed correctly, use LaTeX.

Finally, what do you mean by `order 3'? Do you mean a 3x3 matrix, or a matrix such that ?

Frankly, I believe that row-reduction is the easiest way to find the inverse matrix, even for 3 by 3 and 2 by 2 matrices. However, you can also use the fact that the inverse of the matrix

is given by

where is the "minor" of (note the reversal of i and j). The minor is the determinant of the matrix with the row and column is in removed, multiplied by . This, in fact, will work for any n by n matrix but probably is easier than row-reduction for 2 by 2 and some 3 by 3 matrices.

As a simple 2 by 2 example, if

then the determinant is , the minor of is just , the minor of is , the minor of is , and the minor of is . Remembering the reversal of "i" and "j", the inverse matrix is