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Inverse Matrices

By the way, this process can be used for 3 x 3's and bigger.  (You can only find the inverse of a square matrix.)  BUT, the process gets MUCH stickier!  This is really intended for computers.

Here's the general idea:

A = [ row 1: 2 , -7 , 0 row 2: 3 , 8 , 4 row 3: 5 , 9 , -6 ]
 

Here's the double  matrix:

[ row 1: 2 , -7 , 0 row 2: 3 , 8 , 4 row 3: 5 , 9 , -6 | row 1: 1 , 0 , 0 row 2: 0 , 1 , 0 row 3: 0 , 0 , 1 ] ... the left half is A ... the right half is I
 

Use row operations to get

[ row 1: 1 , 0 , 0 row 2: 0 , 1 , 0 row 3: 0 , 0 , 1 | A^( -1 ) here ]
 

With a lot of VERY careful work, you CAN do it.  (No, you don't have to do it right now.)