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Ex 4.4, 17 (Method 1) Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to A. |A| B. |A|2 C. |A|3 D. 3 |A| We know that |𝑎𝑑𝑗 𝐴| = |𝐴|^(𝑛 − 1) where n is the order of Matrix A Here, n = 3 |𝑎𝑑𝑗 𝐴| = |𝐴|^(3 − 1) = |𝐴|^2 Hence, B is the correct answer Ex 4.4, 17 (Method 2) Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to A. |A| B. |A|2 C. |A|3 D. 3 |A| We know that A (adj A) = |A|I Taking determinants both sides |A (ad jA)| = ||A|I| Solving |A (adj (A))| |A (adj (A))| = |A| |adj (A)| Solving ||A|I| ||A|I| = |A|3|I| = |A|3 Now, |A (ad jA)| = ||A|I| Putting values |A| |adj (A)| = |A|3 |adj (A)| = |A|3/|A| |adj (A)| = |A|2 Thus, B is the correct answer

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo