Explain why multiplying any number by-1 is equivalent to finding the additive inverse of that number

That would be because multiplying any number by a number with an absolute value of 1 gives you a number with the same absolute value (8 * 1 = 8, 56 * - 1 = - 56). Multiplying any number by a negative gives you the opposite sign of the number being multiplied by the negative ( - * - = +, + * - = - ). Therefore, multiplying a number by - 1 gives you both an opposite sign and a number with the same absolute value that you started with.