The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.

The multiplication of all the  Eigen  values is determinant of the matrix. The number of Eigen values of a matrix is equal to number of diagonal elements.

In this case, there are two Eigen values and one of them is $10$. So, the other Eigen values is $50 \div 10 = 5$.
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