How do you find $M^2$ given $M=((2,0), (0, 2))$ ?

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Answer 1 · 2016-05-13T23:38:38

$((4, 0), (0, 4))$

$M = 2I$ is a simple scalar multiple of the $2xx2$ identity matrix.

So $M^2 = (2I)(2I) = 4I^2 = 4I = ((4, 0), (0, 4))$

Scalar multiplication commutes with matrix multiplication.

Answer 2 · 2016-05-13T23:38:44

It is

$M^2=((2,0), (0, 2))*((2,0), (0, 2))=((2*2+0*0,2*0+0*2),(0*2+2*0,0*0+2*2))=((4,0),(0,4))$

How do you find M^2M^2 given M=((2,0), (0, 2))M=((2,0), (0, 2))?