Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:
(a) 4Β Β Β Β Β Β Β (b) 8Β
(c) 64Β Β Β Β Β Β (d) 16
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
Last updated at March 29, 2023 by Teachoo
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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 |π¨^π | = |2π΄| |π¨ Γ π¨| = |2π΄| |π΄||π΄| = |ππ¨| Since order of matrix is 3, using|ππ΄|=π^π |π΄| |π΄||π΄| = π^π |π¨| |π΄||π΄| = 8|π΄| |π΄||π΄| β 8|π΄| = 0 |π΄| (|π΄|β"8" ) = 0 Thus, |π¨| = 0 or |π¨| = 8 Given that A is a non-singular matrix, β΄ |π¨| = 8 Now, |ππ¨| = π^π |π¨| = 8 Γ 8 = 64 So, the correct answer is (C)