# Ex 4.5, 17 - Chapter 4 Class 12 Determinants

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 4.5, 17 (Method 1) Let A be a nonsingular square matrix of order 3 × 3. Then adj A is equal to A. A B. A2 C. A3 D. 3 A We know that 𝑎𝑑𝑗 𝐴 = 𝐴𝑛 − 1 where n is the order of Matrix A Here, n = 3 𝑎𝑑𝑗 𝐴 = 𝐴3 − 1 = 𝐴2 Hence, B is the correct answer Ex 4.5, 17 (Method 2) Let A be a nonsingular square matrix of order 3 × 3. Then adj A is equal to A. A B. A2 C. A3 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)| = A3 A = |A|2 Thus, B is the correct answer

Chapter 4 Class 12 Determinants

Serial order wise

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.