Simplify the Matrix [[a,a],[b,b]][[a,a],[-a,-a]]

$[\begin{array}{c} a & a \\ b & b \end{array}] [\begin{array}{c} a & a \\ - a & - a \end{array}]$

Step 1

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} a \cdot a + a (- a) & a \cdot a + a (- a) \\ b a + b (- a) & b a + b (- a) \end{array}]$

Step 2

Simplify each element of the matrix by multiplying out all the expressions.

Reorder the factors in the terms $b a$ and $b (- a)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & a b - a b \end{array}]$

Subtract $a b$ from $a b$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}]$