I posted the Cramer’s rule for the HP-12c on February 2005.
http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv014.cgi?read=68690
Now I have played with matrices and the HP-12C again.
My old 12C can find the inverse of the 3x3 matrix and pretty quickly too.
Here is my procedure. You may wonder that there is no GTO command in this program. Yes, that´s true. It wasn´t necessary.
01 RCL 5 21 RCL 8 41 RCL 8 61 /
02 RCL 9 22 * 42 * 62 R/S
03 * 23 RCL 5 43 - 63 RCL 5
04 RCL 6 24 RCL 7 43 RCL 0 64 RCL 8
05 RCL 8 25 * 45 / 65 RCL 2
06 * 26 - 46 R/S 66 STO 8
07 - 27 RCL 3 47 RCL 4 67 RDN
08 RCL 1 28 * 48 RCL 7 68 STO 5
09 * 29 + 49 RCL 1 69 RCL 1
10 RCL 6 30 STO 0 50 STO 7 70 *
11 RCL 7 31 RCL 6 51 RDN 71 X<>Y
12 * 32 RCL 9 52 STO 4 72 STO 2
13 RCL 4 33 RCL 3 53 RCL 3 73 RCL 4
14 RCL 9 34 STO 9 54 * 74 *
15 * 35 RDN 55 X<>Y 75 -
16 - 36 STO 6 56 STO 1 76 RCL 0
17 RCL 2 37 RCL 5 57 RCL 6 77 /
18 * 38 * 58 *
19 + 39 X<>Y 59 -
20 RCL 4 40 STO 3 60 RCL 0
User instructions:
Store elements of matrix A in row order into registers R1 through R9. C=A-1. Press R/S to calculate c11.
Press R/S to calculate c21. Press R/S to calculate c31. Press R/S to calculate c12. Press R/S to calculate c22 etc.
You can press RCL 0 to find the determinant of A.