1. Tardigrade
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  3. Mathematics
  4. If the determinant of the matrix A=[0 a b -a 0 β -b α 0] is zero for all a, b then α+β=

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Q. If the determinant of the matrix $A=\begin{bmatrix}0 & a & b \\ -a & 0 & \beta \\ -b & \alpha & 0\end{bmatrix}$ is zero for all $a, b$ then $\alpha+\beta=$

TS EAMCET 2019

Solution:

We have,
$A=\begin{bmatrix} 0 & a & b \\ -a & 0 & \beta \\ -b & \alpha & 0 \end{bmatrix}$
$|A|=0$ for all $a, b$
$\therefore A$ is skew symmetric matrix.
Hence, $\alpha=-\beta \Rightarrow \alpha+ \beta=0$