A=[ 1 2 3; 2 5 3; 1 0 8] A = 1 2 3 2 5 3 1 0 8 inv(A) ans = Columns 1 through 2 -40.0000 16.0000 13.0000 -5.0000 5.0000 -2.0000 Column 3 9.0000 -3.0000 -1.0000 inv(A) ans = -40.0000 16.0000 9.0000 13.0000 -5.0000 -3.0000 5.0000 -2.0000 -1.0000 inv(A)*A ans = 1.0000 0 0 0.0000 1.0000 -0.0000 -0.0000 -0.0000 1.0000 B=eye(3) B = 1 0 0 0 1 0 0 0 1 B*A ans = 1 2 3 2 5 3 1 0 8 B=[ 1 0 0;-2 1 0; 0 0 1] B = 1 0 0 -2 1 0 0 0 1 B*A ans = 1 2 3 0 1 -3 1 0 8 B1=[ 1 0 0;-2 1 0; 0 0 1] B1 = 1 0 0 -2 1 0 0 0 1 B1*A ans = 1 2 3 0 1 -3 1 0 8 B2=[ 1 0 0;0 1 0; -1 0 1] B2 = 1 0 0 0 1 0 -1 0 1 B2*B1*A ans = 1 2 3 0 1 -3 0 -2 5 B3=[ 1 0 0;0 1 0; 0 2 1] B3 = 1 0 0 0 1 0 0 2 1 B3*B2*B1*A ans = 1 2 3 0 1 -3 0 0 -1 B4=[ 1 0 0;0 1 -3; 0 0 1] B4 = 1 0 0 0 1 -3 0 0 1 B4*B3*B2*B1*A ans = 1 2 3 0 1 0 0 0 -1 B5=[ 1 0 3;0 1 0; 0 0 1] B5 = 1 0 3 0 1 0 0 0 1 B5*B4*B3*B2*B1*A ans = 1 2 0 0 1 0 0 0 -1 B6=[ 1 -2 0;0 1 0; 0 0 1] B6 = 1 -2 0 0 1 0 0 0 1 B6*B5*B4*B3*B2*B1*A ans = 1 0 0 0 1 0 0 0 -1 B7=[ 1 0 0;0 1 0; 0 0 -1] B7 = 1 0 0 0 1 0 0 0 -1 B7*B6*B5*B4*B3*B2*B1*A ans = 1 0 0 0 1 0 0 0 1 B7*B6*B5*B4*B3*B2*B1 ans = -40 16 9 13 -5 -3 5 -2 -1 det(B6) ans = 1 det(B5) ans = 1