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KCET2012MathematicsMatrices

Inverse of a diagonal non-singular matrix is

Options

  1. Ascalar matrix
  2. Bskew symmetric matrix
  3. Czero matrix
  4. Ddiagonal matrix

Correct answer

D. diagonal matrix

Step-by-step solution

Let diagonal matrix A= [ array lll a & 0 & 0 0 & a & 0 0 & 0 & a array ] Now, | A |= a ( a ² )= a ³ adj A= [ array ccc a² & 0 & 0 0 & a² & 0 0 & 0 & a² array ] aligned A ⁻¹= adj ( A ) | A | &= 1 a ³ [ array ccc a ² & 0 & 0 0 & a ² & 0 0 & 0 & a ² array ] &= [ array ccc 1 / a & 0 & 0 0 & 1 / a & 0 0 & 0 & 1 / a array ] aligned which is an diagonal matrix.

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