If A is a square matrix of order n, prove that |A adj A| = |A| n .

Question

Philoid · Accepted Answer

|A adj A| = |A|ⁿ

LHS |A adj A|

|A|.|adj A|

|A|.|A|^{n – 1}

|A|^{n – 1 + 1}

|A|ⁿ = RHS

Hence, LHS = RHS