Verify associative property for multiplication of the rational numbers, a, b and c, where a = $\frac{1}{2}$ , b = $\frac{16}{7}$ and c = $\frac{- 21}{8}$

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For each set of rational numbers, given below, verify the associative property of addition of rational numbers:
$(i) \frac{1}{2}, \frac{2}{3} and - \frac{1}{6} (i i) \frac{- 2}{5}, \frac{4}{15} and \frac{- 7}{10} (i i i) \frac{- 7}{9}, \frac{2}{- 3} and \frac{- 5}{18} (i v) - 1, \frac{5}{6} ~ a n d \frac{- 2}{3}$

Q. For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A (BC):
(i)

A = [\begin{matrix} 1 & 2 & 0 \\ - 1 & 0 & 1 \end{matrix}], B = [\begin{matrix} 1 & 0 \\ - 1 & 2 \\ 0 & 3 \end{matrix}] and C = [\begin{matrix} 1 \\ - 1 \end{matrix}]

(ii)

A = [\begin{matrix} 4 & 2 & 3 \\ 1 & 1 & 2 \\ 3 & 0 & 1 \end{matrix}], B = [\begin{matrix} 1 & - 1 & 1 \\ 0 & 1 & 2 \\ 2 & - 1 & 1 \end{matrix}] and C = [\begin{matrix} 1 & 2 & - 1 \\ 3 & 0 & 1 \\ 0 & 0 & 1 \end{matrix}]

Q. Verify commutative property for addition and multiplication of rational numbers using a and b, where a =

\frac{1}{2}

and b =

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Verify the property (a × b) × c = a × (b × c) of rational numbers by using a = $\frac{2}{3}$ , b = $\frac{9}{10}$ and c = $\frac{20}{18}$

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Verify associative property for multiplication of the rational numbers, a, b and c, where a = 12 , b = 167 and c = −218

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Verify associative property for multiplication of the rational numbers, a, b and c, where a = $\frac{1}{2}$ , b = $\frac{16}{7}$ and c = $\frac{- 21}{8}$