1 Binary operations

Let

$${\bf A} = \left( \begin{array}{rr} 3 & 6\\ 2 & 1 \end{array} ... ...rray}{rrrr} 1 & 0 & 3 & 2\\ 0 & -1 & -1 & 1 \end{array}\right)$$

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Form AB.

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Form BA. (Careful, this might be a trick question!)

Let

$${\bf C} = \left( \begin{array}{rr} 3 & 6\\ 2 & 1 \end{array} ... ...D}= \left( \begin{array}{rr} 1 & 2\\ 3 & 4 \end{array} \right)$$

1.

Form ${\bf CD}$.

2.

Form ${\bf DC}$.

3.

In ordinary algebra, multiplication is commutative, i.e. $xy = yx$. In general, is matrix multiplication commutative?

Let

$${\bf E}^{\prime}= \left( \begin{array}{rrr} 1 & 0 & 3\\ 1 & 2 & 1 \end{array} \right)$$

4.

Form ${\bf E(C+D)}$.

5.

Form ${\bf EC + ED}$.

6.

In ordinary algebra, multiplication is distributive over addition, i.e. $x(y+z) = xy + xz$. In general, is matrix multiplication distributive over matrix addition? Is matrix multiplication distributive over matrix subtraction?