Question

Bună ziua! Am nevoie de ajutor la subpunctul c), din subpunctul b) am aflat ca A la a3a=I2

Answer 1

Răspuns:

Explicație pas cu pas:

$A^{3} = I_{2} \\A^{12} = (A^{3})^{4} = (I_{2})^{4} = I_{2}\\A^{23} = A^{21}*A^{2} = (A^{3})^{7}*A^{2} = (I_{2})^{7}*A^{2} = I_{2}*A^{2}=A^{2}\\A^{34} = A^{33}*A = (A^{3})^{11}*A = (I_{2})^{11}*A = I_{2}*A = A$

asadar:

$A^{12} + A^{23} + A^{34} = I_{2} + A^{2} +A = A^{2} + A + I_{2} = 0$ (conform cu subpunctul a)

Answer 2

$A^{12} = A^{4 * 3} = {A ^ {3}} ^ 4 = {I_{2}}^4 = I_{2}$

$A^{23} = A^{3* 7 + 2} = A^{21} * A^{2} = I_{2}^{7} * A^{2} = I_2 * A^{2} = A^{2}$$A^{34} = A^{3* 11 + 1} = A^{33} * A^{1} = I_{2}^{11} * A^{1} = I_2 * A^{1} = A^{1}$

[tex]A^{12} + A ^ {23} + A ^ {34} = A^{2} + A^{1} + I^{1}\\ [/tex]
Conform pct a)$A^{2} + A^{1} + I^{1} = O_2 => A^{12} + A^{23} + A^{34} = O_2$