If A is a square matrix of order 3, such that A ( adj A ) = 10 I , then | adj A | is equal to:

Question

If A is a square matrix of order 3, such that $A (adj A) = 10 I,$ then $| adj A |$ is equal to:

Smart Achievers · Accepted Answer

(3)

Ans. 100

Explanation:

Given: $A (adj A) = 10 I$

We know that, $A . adj A = | A | . I$

$∴$ $| A | = 10$

$∵$ $| adj A | = | A |^{n - 1}$

$∴$ $| adj A |$ $= | A |^{3 - 1} = 10^{2} = 100$

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