AP EAMCET20224 Jul 2022Evening ShiftMathematicsMatricesActual

If A = 1 0 0 a - 1 0 b c 1 is such that A 2 = I , then

Options

Ab = a c 2
Bb = - a c 2
Cb = a + c 2
Db = a c

Correct answer

B. b = - a c 2

Step-by-step solution

Given: A = 1 0 0 a - 1 0 b c 1 And, A 2 = I ⇒ 1 0 0 a - 1 0 b c 1 1 0 0 a - 1 0 b c 1 = 1 0 0 0 1 0 0 0 1 ⇒ 1 0 0 0 1 0 2 b + a c 0 1 = 1 0 0 0 1 0 0 0 1 So, 2 b + a c = 0 ⇒ b = - a c 2

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