Q35 of 74 Page 7

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

|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

Find the matrix X satisfying the equation: .

If , find A^–1 and prove that A² – 4A–5I = O.

If A ^{– 1} = and , find (AB) ^{– 1}.

If , find (A^T) ^{– 1}.

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