Given <em>YA</em> = <em>B</em>, you can solve for <em>Y</em> by multiplying by <em>A </em>⁻¹ on the right (on both sides of the equation). So we have
<em>YA</em> = <em>B</em> ==> (<em>YA</em>) <em>A </em>⁻¹ = <em>BA </em>⁻¹ ==> <em>Y</em> (<em>AA </em>⁻¹) = <em>BA </em>⁻¹ ==> <em>Y</em> = <em>BA </em>⁻¹
provided that the inverse of <em>A</em> exists. In this case, det(<em>A</em>) = 5 ≠ 0, so the inverse does exist, and
Then