DeterminantHard
Question
If A is a square matrix of order n × n and k is a scalar, then adj (kA) is equal to
Options
A.k adj A
B.kn adj A
C.kn -1 adj A
D.kn + 1 adj A
Solution
kA adj (kA) = |kA| In
kA adj (kA) = kn |A| In
kA adj (kA) = kn A adj A
Pre-multiplying A-1
adj (kA) = kn -1 adj A
kA adj (kA) = kn |A| In
kA adj (kA) = kn A adj A
Pre-multiplying A-1
adj (kA) = kn -1 adj A
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