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In your 3rd paragraph, you show a right identity matrix such that AI=A and a left identity matrix (IA=A). The right and left identity matrices are equal only if A is square matrix.

Test your understanding of {unit name}. Bienvenido a la prueba de unidad — ¡donde se ponen a prueba tus habilidades de toda la unidad!

Matrix multiplication is a way of composing linear transformations, and the convention for matrix multiplication is designed to make this composition of linear transformations work correctly.

If A is a square matrix, and you find another matrix B such that AB=I, then you can prove that BA=I as well, and that B=A^ (-1) is the only matrix with this property.