Question: Please help me solving question 1, using two proposition and proof -A is unique. 1/ Using only the properties given in Proposition 2.7 and Proposition

Please help me solving question 1, using two proposition and proof -A is unique.

1/ Using only the properties given in Proposition 2.7 and Proposition 2.10, show -A is unique. Proposition 2.10: Properties of Scalar Multiplication LetA,B be matrices, and k, p be scalars. Then, the following properties hold. ' Distributive Law overMatrix Addition k (A + B) = M + kB - Distributive Law over Scalar Addition (k+p)A =kA+pA 0 Associative Law for Scalar Multiplication k (PA) = (WM 0 Rule for Multiplication by 1 Proposition 2.7: Properties of Matrix Addition LetA,B and C be matrices. Then, the following properties hold. - Commutative Law of Addition A + B = B +A - Associative Law of Addition (A+B)+C=A+(B+C) - Existence of an Additive Identity There exists a zero matrix 0 such that A + 0 = A - Existence of an Additive Inverse There exists a matrix A such that A + (A) = 0

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