**TI86** Program file dated 06/23/04, 19:56  PROPSUP1BooD1/D1/-MATRIX PROPERTIES F1 INVERSE MATRICES F2 TRANSPOSEoD4/D1/-F3 DET()&TRIANGULAR F4 MISCooLD1/-F1/3A/D2/-F2/3C/D3/-F3/3D/D4/-F4/3EoAooD1/D1/-IF A INVERT,K IS POS INT,& C IS SCAL, THENoD3/D1/-(A)=A, (A^k)=AA...A,k FACTORSoD5/D1/-(cA)=(1/c)A (A)=(A)oooD1/D1/-A IS 2x2.A=(ad-bc)*[d b]oD3/D1/-[c a]oD4/D1/-IF B IS A, AB=BA=I (AB)=BAoooD1/D1/-PROOF A UNIQUE: AB=I, AC=I, C(AB)=CI,oD3/D1/-(CA)B=C, IB=C, B=CooBoCooD1/D1/-(A)=A, (cA)=c(A)(A+B)=A+BoD3/D1/-(AB)=BAoD4/D1/-SKEW-SYMET: A=AoooBoDooD1/D1/-det(A)=[j=1,n]a(1,j)C(1,j), C=COFACTORSoD3/D1/-det(AB)=det(A)det(B) det(cA)=c^n det(A)oD5/D1/-det(A)=1/det(A) det(A)=det(A)oD7/D1/-A=(1/det(A))adj(A), x(n)=det(An)/det(A)oooD1/D1/-UP TRI HAS 0s BELOW DIAGONAL.DIAG TRI HAS0sEVERYWHEREoD4/D1/-EXCEPT ON MAIN DIAG. adj(C)=MAT. COFACT CoD6/D1/-IF A=A & n ODD, det A=0, PRF. det A=oD7/D1/-det(AA)&det(A)A =(1)^n det AoD8/D1/-THUS det A=det A, det A=0oooBooEooD1/D1/-A-2A=A(A-2I)oM&