How do you multiply $((3, -2), (-1, 1))$ with $((3, 1), (-2, 4))$ with $((-2, 4), (1, 3))$ ?

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Answer 1 · 2016-11-10T07:17:59

The answer is $=((-31,37),(13,-11))$

The product of two 2x2 matrices is
$((a,b),(c,d))*((e,f),(g,h))=((ae+bg,af+bh),(ce+dg,cf+dh))$

$((3,-2),(-1,1))((3,1),(-2,4))=((9+4,3-8),(-3-2,-1+4))$

$((13,-5),(-5,3))$

and the second multiplication is

$((13,-5),(-5,3))*((-2,4),(1,3))=((-26-5,52-15),(10+3,-20+9))$

$((-31,37),(13,-11))$

How do you multiply ((3, -2), (-1, 1))((3, -2), (-1, 1)) with ((3, 1), (-2, 4))((3, 1), (-2, 4)) with ((-2, 4), (1, 3))((-2, 4), (1, 3))?