math - matrix laws and syntax matlab -

what happening in code? don't understand why getting 2 different different matrices when a^-1 * b^-1 = (a*b)^-1 have tried writing in language keep getting same inequality.

input:

a = [3 5 2; 2 1 -1; 1 2 2];  b = [6 -2 4; 6 4 -12; 12 2 8];  inversea = a^(-1); inverseb = b^(-1);  inversemult = inversea * inverseb; inversematmult = (a*b)^(-1);  equalitycheck = inversemult == inversematmult;  disp(inversemult) disp(inversematmult) disp(equalitycheck) 

output:

   -0.4038   -0.0863    0.1974     0.3224    0.0923   -0.1478    -0.1518   -0.0804    0.0804     -0.0317    0.0615    0.0694     0.1190   -0.2619   -0.1667    -0.0357   -0.0089    0.0625      0     0     0     0     0     0     0     0     0 

you assuming incorrect identity - should be:

(a*b)^-1 = b^-1 * a^-1 

(see useful list of invertible matrix identities here.)

so if change line:

inversematmult = (a*b)^(-1); 

to:

inversematmult = (b*a)^(-1); 

then should expected result. (note equality check may still fail due rounding errors, should see 2 result matrices identical reasonable number of significant figures.)