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Maths-

General

Easy

Question

If A, B and C are three square matrices of the same size such that B = CAC^–1, then CA³C^–1 is equal to -

B
B²
B³
B⁹

The correct answer is: B³

$rightwards double arrow$ BC = CA $therefore$ CA³C^{–1 $rightwards double arrow$}C^–1.B.C.=A= C.A.A.A.C^–1
$rightwards double arrow$ C(C^–1.B.C.)(C^–1.BC)(C^–1.BC).C^–1
$rightwards double arrow$ (±)B.(I).(B).I(B).I = B³

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