Scalarmultiplying to the right Is it commonplace to define scalarmultiplication to the right of a matrix? For example, in my book Linear Algebra and Its applications, David C Lay, I haven't seen it been used once. If s is a scalar and M is a matrix, can't we just define M _s as s_ M ?

It's not often used, but you can define right scalar multiplication of a matrix $M=(m_{ij})_{i,j}$ with a scalar $\lambda$ as $M\cdot \lambda := (m_{ij}\lambda)_{i,j}$. This is equal to $\lambda\cdot M$ in any commutative ring, such as $\mathbb{R}$.