If A is a 3 × 3 matrix such that | A | = 8 , then | 3 A | equals:

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Solution

Q.
If A is a $3 \times 3$ matrix such that $| A |$ $= 8$ , then $| 3 A |$ equals:

1 8

2 24

3 72

4 216

Ans.
(4)

Ans. 216

Explanation:

Given:    $| A |$ $= 8$

We know that,   $| k A |$ $= k^{n}$ $| A |$ $,$ where $k$ is a constant

$∴$        $| 3 A |$ $= 3^{3}$ $| A |$ $= 27 \times 8 = 216$

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