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Question 1063250: If A is a square matrix of order 3 such that |A|=5 find|A adj A|
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! I assume you mean |A adj A| is |A adj(A)|
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n = 3
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Note that A adj(A) = |A|(I)
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|A(adj A)| = |(|A| I)|
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|A| |adj A| = |A|^n * |I|
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Note that for constant k, |kA| = k^n |A| and
|(|A|I)| = |A|^n |I| = |A|^n
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|A| |adj A| = |A|^n
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we know that |A| not equal to 0
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|adj A| = |A|^(n-1)
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|A adj(A)| = 5 * 5^(3-1) = 125
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