Question:

Let A be a 3x3 matrix such that A × ⎡⎢⎣123023011⎤⎥⎦ = ⎡⎢⎣001100010⎤⎥⎦. Then A⁻¹ is :

⎡⎢⎣321320110⎤⎥⎦

⎡⎢⎣013023111⎤⎥⎦

⎡⎢⎣312302101⎤⎥⎦

⎡⎢⎣123011023⎤⎥⎦

A × ⎡⎢⎣123023011⎤⎥⎦ = ⎡⎢⎣001100010⎤⎥⎦
Row R3 ↔ R1, R2 ↔ R3
A × ⎡⎢⎣312302101⎤⎥⎦ = ⎡⎢⎣100010001⎤⎥⎦ = I
∴ A⁻¹ = ⎡⎢⎣312302101⎤⎥⎦