State True or False for the statements
(A³)^-1 = (A^-1)³, where A is a square matrix and |A| ≠ 0.

Question

State True or False for the statements (A 3 ) -1 = (A -1 ) 3 , where A is a square matrix and |A| ≠ 0.

Philoid · Accepted Answer

True

We know that (Aⁿ)^-1 = (A^-1)ⁿ, where n ∈ N.

∴ (A³)^-1 = (A^-1)³

State True or False for the statements(A3)-1 = (A-1)3, where A is a square matrix and |A| ≠ 0.