Question 549623
<pre>
The way to multiply two 2×2 matrices is like this:

{{{(matrix(2,2,a,b,c,d))}}}{{{(matrix(2,2,e,f,g,h))}}} = {{{(matrix(2,2,ae+bg,af+bh,ce+dg,cf+dh))}}}

Use that rule to multiply the two 2×2 matrices on the left:

{{{(matrix(2,2,x,y,z,4))}}}{{{(matrix(2,2,0,1,3,4))}}} = {{{(matrix(2,2,6,13,12,13))}}}

{{{(matrix(2,2,x*0+y*3,x*1+y*4,z*0+4*3,z*1+4*4))}}} = {{{(matrix(2,2,6,13,12,13))}}}

{{{(matrix(2,2,3y,x+4y,12,z+16))}}} = {{{(matrix(2,2,6,13,12,13))}}}

Equate corresponding elements of the matrices on the left
and right:

{{{system(3y=6,x+4y=13,12=12,z+16=13)}}}

From those you get x=5, y = 2, z = -3

Edwin</pre>