Laws Of Matrix And Multiple

p {margin: 0; padding: 0;} NO Date Laws of Matrix Addition and Matrix Multiple 1) Matrix multiplication is generally not commutative that is, AB + BA even f BA is confarable (Because diff dot product of rows or col of A&B) A. 12 8 0-1 34 67 4B ((0)+2(6) (-1/+2(7) = 12 13 3(0)+4(6) 3(-1)+4(7) 24 25 BA = 0(1)+(+))(3) 0(2)+(-1)4 -3-4 2 (6(1)+7(3) 6(2)+(7)4 27 40 2) Exceptions to non-communicative law AB = BA IFF B= a sclair B= identity matrix.I or B= the inverse of A i.e. A' 3) Theorem It is not true that AB AC B = C Proof : 121 212 4 10-1 B = 0 0 C= 1-1 / -2-3 231 Note: IF AB ? 4c for all matrices, A,then B=C