The trace is one and determinant is two. Cayley–Hamilton therefore gives A²−A+2I=0, or A²=A−2I. Comparing with the given relation yields k=1, A. Direct multiplication gives [[1,−2],[4,−4]] and confirms it.
More Linear Algebra questions
GATE 2021 BM Q36– A nonsingular 2×2 matrix A has trace 12 and determinant 32. Find the eigenvalues of A⁻¹.
GATE 2020 BM Q27– A nonsingular 3×3 matrix P has eigenvalues 1,2,3. Find trace(P⁻¹), to two decimals.
GATE 2026 BM Q15– Find the eigenvalues of P=pmatrix1&-2\\3&-4pmatrix.
GATE 2026 BM Q18– Invertible n×n matrix P satisfies P³=I. Which must hold?
GATE 2026 BM Q58– Vector (2,a)T is an eigenvector for the smallest eigenvalue of pmatrix1&2\\2&1pmatrix.…
GATE 2025 BM Q17– A 3×3 matrix M has determinant 8. Multiply every element by −2. Find the new determinant.