8.
a) `[(1, 2), (-1, 0), (3, 1)]*[(1, 4), (2, -3)] = [(1*1+2*2, 1*4+2*(-3)), ((-1)*1+0*2, (-1)*4+0*(-3)), (3*1+1*2, 3*4+1*(-3))] = [(5, -2), (-1, -4), (5, 9)]`
b) `[(1, -1, 3)]*[(-2, 3), (1, 2), (-1, -4)] = [(1*(-2)+(-1)*1+3*(-1), 1*3+(-1)*2+3*(-4))] = [(-6, -11)]`
c) `[(4, 1), (2, 2)]^5 = [(4, 1), (2, 2)]*[(4, 1), (2, 2)]*[(4, 1), (2, 2)]*[(4, 1), (2, 2)]*[(4, 1), (2, 2)] ``=`` [(4*4+1*2, 4*1+1*2), (2*4+2*2, 2*1+2*2)]*[(4, 1), (2, 2)]*[(4, 1), (2, 2)]*[(4, 1), (2, 2)] =`
`=`` [(18, 6), (12, 6)]*[(18, 6), (12, 6)]*[(4, 1), (2, 2)] ``=`` [(18*18+6*12, 18*6+6*6), (12*18+6*12, 12*6+6*6)]*[(4, 1), (2, 2)] ``=`` [(396, 144), (288, 108)]*[(4, 1), (2, 2)] =`
`=`` [(396*4+144*2, 396*1+144*2), (288*4+108*2, 288*1+108*2)] ``=`` [(1872, 684), (1368, 504)] ``=`` 36[(52, 19), (38, 14)]`
9.
`A = [(1, 2, -1), (0, 1, 2)] " " B = [(-1, 0, 2), (2, 1, 2), (5, -1, 3)]`
`A*B = [(1*(-1)+2*2+(-1)*5, 1*0+2*1+(-1)*(-1), 1*2+2*2+(-1)*3), (0*(-1)+1*2+2*5, 0*0+1*1+2*(-1), 0*2+1*2+2*3)] ``=`` [(-2, 3, 3), (12, -1, 8)]`
A `B*A` nem értelmezett, mert `B` oszlopainak száma nem egyenlő `A` sorainak számával.
10.
`A = [(1, -1, 0), (2, 1, 3), (4, -3, 2)] " " B = [(0, 2, -4), (1, -1, 0), (2, 0, -3)]`
`A*B = [(1*0+(-1)*1+0*2, 1*2+(-1)*(-1)+0*0, 1*(-4)+(-1)*0+0*(-3)), (2*0+1*1+3*2, 2*2+1*(-1)+3*0, 2*(-4)+1*0+3*(-3)), (4*0+(-3)*1+2*2, 4*2+(-3)*(-1)+2*0, 4*(-4)+(-3)*0+2*(-3))] ``=`` [(-1, 3, -4), (7, 3, -17), (1, 11, -22)]`
`B*A = [(0*1+2*2+(-4)*4, 0*(-1)+2*1+(-4)*(-3), 0*0+2*3+(-4)*2), (1*1+(-1)*2+0*4, 1*(-1)+(-1)*1+0*(-3), 1*0+(-1)*3+0*2), (2*1+0*2+(-3)*4, 2*(-1)+0*1+(-3)*(-3), 2*0+0*3+(-3)*2)] ``=`` [(-12, 14, -2), (-1, -2, -3), (-10, 7, -6)]`
`A*(A-B) = A^2-A*B`
`A^2 = [(1*1+(-1)*2+0*4, 1*(-1)+(-1)*1+0*(-3), 1*0+(-1)*3+0*2), (2*1+1*2+3*4, 2*(-1)+1*1+3*(-3), 2*0+1*3+3*2), (4*1+(-3)*2+2*4, 4*(-1)+(-3)*1+2*(-3), 4*0+(-3)*3+2*2)] ``=`` [(-1, -2, -3), (16, -10, 9), (6, -13, -5)]`
`A*(A-B) = A^2-A*B ``=`` [(-1, -2, -3), (16, -10, 9), (6, -13, -5)]-[(-1, 3, -4), (7, 3, -17), (1, 11, -22)] ``=`` [(0, -5, 1), (9, -13, 26), (5, -24, 17)]`
`B*(B-A) = B^2-B*A`
`B^2 = [(0*0+2*1+(-4)*2, 0*2+2*(-1)+(-4)*0, 0*(-4)+2*0+(-4)*(-3)), (1*0+(-1)*1+0*2, 1*2+(-1)*(-1)+0*0, 1*(-4)+(-1)*0+0*(-3)), (2*0+0*1+(-3)*2, 2*2+0*(-1)+(-3)*0, 2*(-4)+0*0+(-3)*(-3))] ``=`` [(-6, -2, 12), (-1, 3, -4), (-6, 4, 1)]`
`B*(B-A) = B^2-B*A = [(-6, -2, 12), (-1, 3, -4), (-6, 4, 1)]-[(-12, 14, -2), (-1, -2, -3), (-10, 7, -6)] ``=`` [(6, -16, 14), (0, 5, -1), (4, -3, 7)]`
`A^2-B^2 = [(-1, -2, -3), (16, -10, 9), (6, -13, -5)]-[(-6, -2, 12), (-1, 3, -4), (-6, 4, 1)] = [(5, 0, -15), (17, -13, 13), (12, -17, -6)]`
Remélem érthető ahogy csinálom és önállóan is menni fog!