$\"\"$

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Associative property of scalar multiplication : $\"\"$ and $\"\"$ .

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Now prove $\"\"$ for any $\"\"$ matrix.

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Consider $\"\"$ matrix as $\"\"$ , $\"\"$ and $\"\"$ .

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Conisder $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Conisder $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Associative property of scalar multiplication $\"\"$ matrix is satisfied.