Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:
(a) 4 (b) 8
(c) 64 (d) 16
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Last updated at Sept. 4, 2021 by Teachoo
Transcript
Question 28 Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is: (a) 4 (b) 8 (c) 64 (d) 16 Given A2 = 2A Taking Determinant both sides |๐จ^๐ | = |2๐ด| |๐จ ร ๐จ| = |2๐ด| |๐ด||๐ด| = |๐๐จ| Since order of matrix is 3, using|๐๐ด|=๐^๐ |๐ด| |๐ด||๐ด| = ๐^๐ |๐จ| |๐ด||๐ด| = 8|๐ด| |๐ด||๐ด| โ 8|๐ด| = 0 |๐ด| (|๐ด|โ"8" ) = 0 Thus, |๐จ| = 0 or |๐จ| = 8 Given that A is a non-singular matrix, โด |๐จ| = 8 Now, |๐๐จ| = ๐^๐ |๐จ| = 8 ร 8 = 64 So, the correct answer is (C)
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