MATRICES & DETERMINANTS: JEE ADVANCED PRACTICE QUESTIONS AND CONCEPTS 2025/2026 What is the condition for the product of two symmetric matrices M and N to be symmetric? - ANS-The product MN is symmetric if M and N commute (MN = NM). What does it mean if MN - NM is skew symmetric for symmetric matrices M and N? - ANS-It means that the difference between the products of the matrices in different orders results in a skew symmetric matrix. What is the condition for a 2×2 symmetric matrix M with integer entries to be invertible? - ANS-M is invertible if the product of entries in the main diagonal is non-zero. What is the determinant condition for the matrix (M² + MN²) if M and N are 3×3 matrices that commute?
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