a)
If X=( X1 X2 )
( X3 X4 )
and
Y=( Y1 Y2 )
( Y3 Y4 )
then X × Y=( X1Y1+X2Y3 X1Y2+X2Y4 )
( X3Y1+X4Y3 X3Y2+X4Y4 )
A²=( 44 60 )
( 84 116 )
B²=( 28 40 )
( 60 88 )
A²-B²=( 16 20 )
( 24 28 )
b)
A-B=( 1 1 )
( 1 1 )
A+B=( 5 9 )
( 13 17 )
(A-B)(A+B)=( 18 26 )
( 18 26 )
c)
(A+B)(A-B)=( 14 30 )
( 14 30 )
d)
AB=( 36 52 )
( 68 100)
BA=( 34 46 )
( 74 102 )
A²+AB-BA-B²=( 44+36-33-28 60+36-46-40 )
( 84+68-74-60 116+100-102-88 )
=( 19 10 )
( 18 26 )