Question

Is determinant greater than 0 is sufficient condition for the matrix to be positive definate?

Answer 1

On the other hand if the determinant ispositive, then either (i) both eigenvalues are positive, or (ii) both eigenvalues are negative. ... Therefore, a necessary and sufficient conditionfor the quadratic form of a symmetric 2 × 2 matrix to be positive definite is for det(A) > 0 and a > 0.