If A is an involuntary matrix given by A = 0 1 - 1 4 - 3 4 3 - 3 4 then the inverse of A 2 will be

If A is an involuntary matrix given by A=01-14-343-34 then the inverse of A2 will be
  1. 2A
  2. A-12
  3. A2
  4. A2

Solution

Given: \(A\) is involutary \(\Rightarrow A^2=I \Longrightarrow A^{-1}=A\) We need: \(\left(\frac{A}{2}\right)^{-1}\) Property: \((c A)^{-1}=\frac{1}{c} A^{-1}\) So, \(\left(\frac{A}{2}\right)^{-1}=2 A^{-1}=2 A\)

Asked in: MHT CET Full Test 8

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