NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given M = bmatrix 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 bmatrix The determinant of the diagonal matrix M is |M| = 2 2 2 = 8. For a square matrix of order n, the determinant of its adjoint is given by | adj M| = |M|^ n-1 . Since the order of M is n = 3, we have | adj M| = |M|^ 3-1 = |M|^2. The required value is |M| \, | adj M| = |M| |M|^2 = |M|^3. Substituting |M| = 8, we get 8^3 = 512. Answer: 512