Let A be a 3 $\times$ 3 real matrix. If det(2Adj(2 Adj(Adj(2A)))) = 241, then the value of det(A2) equal __________.
Answer (integer)
4
Solution
adj (2A) = 2<sup>2</sup> adjA<br><br>$\Rightarrow$ adj(adj (2A)) = adj(4 adjA) = 16 adj (adj A)<br><br>= 16 | A | A<br><br>$\Rightarrow$ adj (32 | A | A) = (32 | A |)<sup>2</sup> adj A<br><br>12(32| A |)<sup>2</sup> |adj A | = 2<sup>3</sup> (32 | A |)<sup>6</sup> | adj A |<br><br>2<sup>3</sup> . 2<sup>30</sup> | A |<sup>6</sup> . | A |<sup>2</sup> = 2<sup>41</sup><br><br>| A |<sup>8</sup> = 2<sup>8</sup> $\Rightarrow$ | A | = $\pm$2<br><br>| A |<sup>2</sup> = | A |<sup>2</sup> = 4
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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