2.2.1—Matrix equations

A matrix equation such as AX=B is solved by multiplying by A⁻¹ on the correct side when A is square and invertible: X=A⁻¹B. For systems, row reduction can avoid forming an inverse.

Check dimensions before multiplying, and interpret a singular matrix as a possible no-solution or many-solution case rather than forcing an inverse.

If A is 2×2 and AX=B, compute X=A⁻¹B and verify by multiplying AX back to B. If det A=0, use row reduction to test consistency instead.

Matrix division is not scalar division, and multiplying by A⁻¹ on the right generally solves a different equation.