Question

If A and B are square matrices of the same order and AB = 3I, then A^-1 = __________________.

Answer 1

Given:
A and B are square matrices of the same order
AB = 3I


AB = 3I
Pre-Multiplying both sides by A⁻¹, we get
⇒ A⁻¹(AB) = A⁻¹(3I)
⇒ (A⁻¹A)B = 3(A⁻¹I)
⇒ (I)B = 3A⁻¹
⇒ B = 3A⁻¹
⇒ $\frac{1}{3}B$ = A⁻¹

Hence, if A and B are square matrices of the same order and AB = 3I, then A⁻¹ = $\underline{\frac{1}{3}B}$.