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If A is a square matrix of order 3 and |A| = -5, then |3A| is equal to

Solution

✅ Correct Option: 1

Given that AA is a square matrix of order 3 and ∣A∣=−5|A| = -5.

For a square matrix of order nn, when multiplying by a scalar kk:

∣kA∣=kn×∣A∣|kA| = k^n \times |A|


Here, the matrix AA has order n=3n = 3 and the scalar is k=3k = 3.

Applying the formula:

∣3A∣=33×∣A∣|3A| = 3^3 \times |A|

∣3A∣=27×(−5)|3A| = 27 \times (-5)

∣3A∣=−135|3A| = -135


Note: The scalar must be raised to the power of the matrix order. A common error is calculating ∣3A∣=3×(−5)=−15|3A| = 3 \times (-5) = -15, which is incorrect.

Therefore, ∣3A∣=−135|3A| = -135.

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