% non-singular matrix
b=[7110.327, -2592.219, 631.419, -288.541, 169.250, -113.431, 82.646, -63.812, 51.448, -42.914, 36.804, -32.315, 28.958, -26.424, 24.511, -23.083, 22.050, -21.350, 20.944;
 -1218.551, 1508.124, -720.486, 169.250, -74.433, 42.572, -28.131, 20.364, -15.701, 12.683, -10.624, 9.164, -8.102, 7.317, -6.734, 6.304, -5.996, 5.789, -5.669;
 169.250, -482.641, 674.499, -350.244, 82.646, -36.010, 20.364, -13.333, 9.592, -7.371, 5.950, -4.991, 4.320, -3.838, 3.488, -3.235, 3.056, -2.936, 2.868;
 -49.544, 82.646, -268.958, 399.001, -215.550, 51.448, -22.463, 12.683, -8.285, 5.950, -4.571, 3.694, -3.108, 2.702, -2.415, 2.211, -2.069, 1.976, -1.923;
 20.364, -27.810, 51.448, -178.696, 275.664, -152.325, 36.804, -16.173, 9.164, -6.000, 4.320, -3.329, 2.702, -2.285, 2.000, -1.803, 1.668, -1.580, 1.531;
 -10.260, 12.683, -18.791, 36.804, -132.946, 211.205, -118.438, 28.958, -12.831, 7.317, -4.818, 3.488, -2.705, 2.211, -1.886, 1.668, -1.522, 1.428, -1.376;
 5.950, -6.944, 9.164, -14.257, 28.958, -107.451, 174.780, -99.104, 24.511, -10.963, 6.304, -4.185, 3.056, -2.392, 1.976, -1.707, 1.531, -1.420, 1.359;
 -3.839, 4.320, -5.318, 7.317, -11.762, 24.511, -92.803, 153.928, -88.144, 22.050, -9.966, 5.789, -3.883, 2.868, -2.273, 1.906, -1.674, 1.531, -1.453;
 2.702, -2.966, 3.488, -4.451, 6.304, -10.377, 22.050, -84.854, 143.052, -82.752, 20.944, -9.576, 5.630, -3.826, 2.868, -2.312, 1.976, -1.775, 1.668;
 -2.050, 2.211, -2.519, 3.056, -4.000, 5.789, -9.704, 20.944, -81.727, 139.664, -81.727, 20.944, -9.704, 5.789, -4.000, 3.056, -2.519, 2.211, -2.050;
 1.668, -1.775, 1.976, -2.312, 2.868, -3.826, 5.630, -9.576, 20.944, -82.752, 143.052, -84.854, 22.050, -10.377, 6.304, -4.451, 3.488, -2.966, 2.702;
 -1.453, 1.531, -1.674, 1.906, -2.273, 2.868, -3.883, 5.789, -9.966, 22.050, -88.144, 153.928, -92.803, 24.511, -11.762, 7.317, -5.318, 4.320, -3.839;
 1.359, -1.420, 1.531, -1.707, 1.976, -2.392, 3.056, -4.185, 6.304, -10.963, 24.511, -99.104, 174.780, -107.451, 28.958, -14.257, 9.164, -6.944, 5.950;
 -1.376, 1.428, -1.522, 1.668, -1.886, 2.211, -2.705, 3.488, -4.818, 7.317, -12.831, 28.958, -118.438, 211.205, -132.946, 36.804, -18.791, 12.683, -10.260;
 1.531, -1.580, 1.668, -1.803, 2.000, -2.285, 2.702, -3.329, 4.320, -6.000, 9.164, -16.173, 36.804, -152.325, 275.664, -178.696, 51.448, -27.810, 20.364;
 -1.923, 1.976, -2.069, 2.211, -2.415, 2.702, -3.108, 3.694, -4.571, 5.950, -8.285, 12.683, -22.463, 51.448, -215.550, 399.001, -268.958, 82.646, -49.544;
 2.868, -2.936, 3.056, -3.235, 3.488, -3.838, 4.320, -4.991, 5.950, -7.371, 9.592, -13.333, 20.364, -36.010, 82.646, -350.244, 674.499, -482.641, 169.250;
 -5.669, 5.789, -5.996, 6.304, -6.734, 7.317, -8.102, 9.164, -10.624, 12.683, -15.701, 20.364, -28.131, 42.572, -74.433, 169.250, -720.486, 1508.124, -1218.551;
 20.944, -21.350, 22.050, -23.083, 24.511, -26.424, 28.958, -32.315, 36.804, -42.914, 51.448, -63.812, 82.646, -113.431, 169.250, -288.541, 631.419, -2592.219, 7110.327];
sizeb=n=size(b,1)
rankb=rank(b)
% Builds blocked matrix
B=[b zeros(n); zeros(n) eye(n)];
% Computes inverse
inv1=inv(B);
% Computes invese by blocks: non-trivial block:
invb=inv(b);
% Build inverse
inv2=[invb zeros(n); zeros(n) eye(n)];
% Both inverse matrices should be equal
diffinvs=norm(inv1-inv2)
% All these condition numbers should be 1
cond(inv1*B)
cond(B*inv1)
cond(inv2*B)
cond(B*inv2)
% Check also with another ordering
B_=[eye(n) zeros(n); zeros(n) b];
% use inv function
inv1_=inv(B_);
%invb=inv(b);
% Build inverse by blocks
inv2_=[eye(n) zeros(n); zeros(n) invb];
% Both inverse matrices should be equal
diffinvs_=norm(inv1-inv2)
% All these condition numbers should be 1
cond(inv1_*B_)
cond(B_*inv1_)
cond(inv2_*B_)
cond(B_*inv2_)