AP EAMCET201822 Apr 2018Evening ShiftMathematicsMatricesActual

If A is a square matrix of order 3 and A^2+A+2 I=0 , then

Options

AA can not be a skew-symmetric matrix
B|A+I|=0
CA is non singular and A⁻¹=(A+I)⁻¹
D|A||A+I|=2

Correct answer

A. A can not be a skew-symmetric matrix

Step-by-step solution

Given matrix equation A^2+A+2 I=0 A(A+I)=-2 I array lc & |A(A+I)|=|-2 I| & |A||A+I|=(-2)^3 & |A||(A+I)|=-8 & |A| 0 and |A+I| 0 array and the determinant of skew-symmetric matrix. having odd order is zero. By here |A| 0 . So, A can not be a skew-symmetric matrix.

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