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AP EAMCET202021 Sep 2020Morning ShiftMathematicsMatricesActual

Let (a, b R - 0 ), and (I₂ ) be the identity matrix of order 2. Then the rank of the (block) matrix ( [ array ll a I₂ & b₂ a I₂ & b I₂ array ] ) is

Options

  1. A2
  2. B1
  3. C4
  4. D3

Correct answer

A. 2

Step-by-step solution

Since (a, b R - 0 ) and (I₂ ) is a identify matrix of order 2 . Then the block matrix ( [ array ll a I₂ & b I₂ a I₂ & b I₂ array ] ) is a non-singular matrix, so the rank of the given block matrix is 2.

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