A is a scalar matrix with scalar k ≠ 0 of order 3. Then A-¹ is
From the definition, A=kI₃. Inverse formula (kI)⁻¹=(1/k)I. Because kI×(1/k)I=I₃. So answer (1/k)I. Full solution.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
#scalar matrix
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