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Scalar Matrix

Let A be a 3×...

Question

Let $A$ be a $3 \times 3$ matrix and $A^{T}$ be transpose matrix of $A .$ If $A = 3 A^{T} - 4 I,$ where $I$ is identity matrix of order $3,$ then $det (A)$ is equal to

A

2

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B

5

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C

8

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D

10

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Solution

The correct option is C $8$
$A = 3 A^{T} - 4 I$
Since $A^{T} = 3 A - 4 I$
$∴ A = 3 (3 A - 4 I) - 4 I$
$\Rightarrow A = 9 A - 16 I$
$\Rightarrow A = 2 I$
$\Rightarrow | A | = | 2 I | = 2^{3} \cdot 1 = 8$

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