Question

Let Upper A equals left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 2 2nd Column 4 2nd Row 1st Column 1 2nd Column 3 EndMatrix right bracketA=

−2 4
1 3
​, and Upper B equals left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 2 2nd Column 1 2nd Row 1st Column 3 2nd Column 7 EndMatrix right bracketB=

−2 1
3 7
.a. Find

ABAB​,

if possible. b. Find

BABA​,

if possible.

c. Are the answers in parts a and b the ​same?

d. In​ general, for matrices A and B such that AB and BA both​ exist, does AB always equal​ BA?

a. Find

ABAB​,

if possible.

Answer 1

not

Explanation:

`\left[\begin{array}{ccc}-2&4\\1&3\end{array}\right] *\left[\begin{array}{ccc}-2&1\\3&7\end{array}\right]=`

First is A and Second is B

Let's find A*B

`\left[\begin{array}{ccc}-2(-2)+4*3&-2*1+4*7\\1(-2)+3*3&1*1+3*7\end{array}\right] =\left[\begin{array}{ccc}16&26\\7&22\end{array}\right]`

b)

`\left[\begin{array}{ccc}-2&1\\3&7\end{array}\right] \left[\begin{array}{ccc}-2&4\\1&3\end{array}\right] =`

Now let's find B*A

`\left[\begin{array}{ccc}-2(-2)+1*1&-2*4+1*3\\3(-2)+7*1&3*4+7*3\end{array}\right] =\left[\begin{array}{ccc}5&-5\\1&23\end{array}\right]`

c) They are not