# if A= 1 2 3 4 and B= 2 1 1 2

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if
A=
|1 2|
| 3 4|
and
B=
| 2 -1|
| 1 2 |
AB-B^2 =
???
Solution
a=1 b=2 c=3 d=4 e=2 f=-1 g=1 h=2 abcd = matrix A
efgh=matrix B
A * B =
| a b| |e f | |(ae + bg) (af + bh) | = |4 3|

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|c d| |g h | |(ce + dg) (cf + dh) | = |10 5|
B * B (B^2) =
|e f| |e f| |(ee +fg) (ef + fh) | = |3 -4|
|g h| |g h| |(ge + hg) (gf + hh)| = |4 3|
AB B^2
|4 3| |3 -4| (distribute the negative sign)
|10 5| - |4 3 |
= |4 3| |-3 4| (distribute the negative sign)
|10 5| + |-4 -3 |
= |1 7| (now you can just add.[4+ (-3) = 1], [3+4=7],
[10+(-4)=6], & [5+(-3)=2]
|6 2|

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if A= |1 2| | 3 4| and B= | 2 -1| | 1 2 | AB-B^2 = ??? Solution a=1 b=2 c=3 d=4 e=2 f=-1 g=1 h=2 abcd = matrix A efgh=matrix B A * B = | a b| |e f | |(ae + bg) (af + bh) | = |4 3| |c d| |g h | |(ce + dg) (cf + dh) | = |10 5| B * B (B^2) = |e f| |e f| |(ee +fg) (ef + fh) | = |3 -4| |g h| |g h| |(ge + hg) (gf + hh)| = |4 3| AB – B^2 |4 3| |3 -4| (distribute the negative sign) |10 5| - |4 3 | = |4 3| |-3 4| (distribute the negative sign) |10 5| + |-4 -3 | = |1 7| (now you can just add….[4+ ( -3) = 1], [3+4=7], [10+(-4)=6], & [5+(-3)=2] |6 2| hope this helps....please rate :-) Name: Description: ...
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