Chapter 1.6, Problem 19E

(a)

To determine

To prove: Let $a$ and $b$ be real numbers and $A$ is element of $M_{m\times n}\left(ℝ\right)$, then $a(bA)=(ab)A$.

(b)

To determine

To prove: Let $a$ be real number and $A$ and $B$ are elements of $M_{m\times n}\left(ℝ\right)$, then $a(A+B)=aA+aB$.

(c)

To determine

To prove: Let $a$ and $b$ be real numbers and $A$ is element of $M_{m\times n}\left(ℝ\right)$, then $(a+b)A=aA+bA$.