Question

If A is 3 × 3 invertible matrix, then show that for any scalar k (non-zero), kA is invertible and (kA)^–1 =(1/k)A^-1

Answer 1

We have,

Hence (kA) is inverse of (1/k)A^-1

^{or,  (kA)–1 =(1/k)A-1}