Given that A is a non-singular matrix of order 3 such that A2 = 2A, th

1.	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
Answer» Option : (c) \(A^2=2A\) \(\Rightarrow\|A^2\|=\|2A\|\) \(\Rightarrow\|A^2\|=2^3\|A\|\) \(as\,\|kA\|=k^n\|A\|\) for a matrix of order n \(\Rightarrow\) either \|A\| = 0 or \|A\| = 8 But A is non-singular matrix \(\therefore\|2A\|=2^3\|A\|=8^2=64 \)

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

Answer»

Option : (c)

\(A^2=2A\)

\(\Rightarrow|A^2|=|2A|\)

\(\Rightarrow|A^2|=2^3|A|\)

\(as\,|kA|=k^n|A|\) for a matrix of order n

\(\Rightarrow\) either |A| = 0 or |A| = 8

But A is non-singular matrix

\(\therefore|2A|=2^3|A|=8^2=64 \)

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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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