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Ex 4.5, 18 - If A is an invertible matrix of order 2, det(A-1)

Ex 4.5, 18 - Chapter 4 Class 12 Determinants - Part 2

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Ex 4.5, 18 If A is an invertible matrix of order 2, then det(A−1) is equal to A. det (A) B. 1/(det (A)) C. 1 D. 0 We know that AA-1 = I Taking determinant both sides |"AA−1" |= |I| |A| |A-1| = |I| |A| |A-1| = 1 |A-1| = 1/(|A|) Since |A| ≠ 0 (|AB| = |A| |B|) ( |I| = 1) Hence, |A-1| = 1/(|A|) is valid Thus, the correct answer is B

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