To solve a matrix equation we follow the normal order of operations with the added restriction that multiplication and division need to happen in the order that they are written, since for matrices, #AB !=BA# in general (there are special cases where this is true).

So for our equation, #A-2B#, we need to start with the multiplication #2B#. Multiplying a scalar, #2#, by a matrix, #B#, has the effect of multiplying each of the matrix elements by the scalar, therefore,

#2B = 2*((-4, 3), (5, -2)) = ((-8, 6), (10, -4))#

subtracting two matrices requires that each matrix have the same dimensions - this is true in our case since #A# and #B# are both #2xx2# matrices. Subtracting matrices results in the subtraction of each element from the corresponding element in the other matrix, i.e.

#((a_(11), a_(12)), (a_(21), a_(22)))-((b_(11), b_(12)), (b_(21), b_(22))) = ((a_(11)-b_(11), a_(12)-b_(12)), (a_(21)-b_(21), a_(22)-b_(22)))#

in our case

#A-2B=((-1, 2), (3, 4))-((-8, 6), (10, -4)) = ((7, -4), (-7, 8))#