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Question: Answered & Verified by Expert
Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{\mathrm{m} \times \mathrm{m}}$ be a matrix and $\mathrm{C}=\left[\mathrm{c}_{\mathrm{iij}}\right]_{\mathrm{m} \times \mathrm{m}}$ be another matrix where $\mathrm{c}_{\mathrm{ij}}$ is the cofactor of $\mathrm{a}_{\mathrm{ij}}$. Then, what is the value of $|\mathrm{AC}|$?
MathematicsMatricesNDANDA 2007 (Phase 2)
Options:
  • A $|\mathrm{A}|^{\mathrm{m}-1}$
  • B $|\mathrm{A}|^{\mathrm{m}}$
  • C $|\mathrm{A}|^{\mathrm{m}+1}$
  • D Zero
Solution:
1337 Upvotes Verified Answer
The correct answer is: $|\mathrm{A}|^{\mathrm{m}+1}$
Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{i} j}\right]_{\mathrm{m} \times \mathrm{m}}$ be a matrix and $\mathrm{C}=\left[\mathrm{c}_{\mathrm{i} j}\right]_{\mathrm{m} \times \mathrm{m}}$ be
another matrix where cij is the cofactor of $\mathrm{a}_{\mathrm{ij}}$
$\therefore \quad$ The value of $|\mathrm{AC}|=|\mathrm{A}|^{\mathrm{m}+1}$

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