Question 189003
<pre><font size = 4 color = "indigo"><b>
{{{(matrix(2,2,2,1,5,3))X = (matrix(2,2,4,3,3,2))}}}

The inverse of {{{(matrix(2,2,2,1,5,3))}}} is {{{(matrix(2,2,3,-1,-5,2))}}}
So we left-multiply both sides by this inverse:

{{{(matrix(2,2,3,-1,-5,2))
(matrix(2,2,2,1,5,3))X = 
(matrix(2,2,3,-1,-5,2))
(matrix(2,2,4,3,3,2))}}}

{{{(matrix(2,2,(3)(2)+(-1)(5),(3)(1)+(-1)(3),(-5)(2)+(2)(5),(-5)(1)+(2)(3)))X = 
(matrix(2,2,(3)(4)+(-1)(3),(3)(3)+(-1)(2),(-5)(4)+(2)(3),(-5)(3)+(2)(2)))}}}

{{{(matrix(2,2,6-5,3-3,-10+10,-5+6))X = 
(matrix(2,2,12-3,9-2,-20+6,-15+4))}}}

{{{(matrix(2,2,1,0,0,1))X = 
(matrix(2,2,9,7,-14,-11))
}}}

{{{X = (matrix(2,2,9,7,-14,-11))}}}

-----

Check:

{{{(matrix(2,2,2,1,5,3))X = (matrix(2,2,4,3,3,2))}}}

{{{(matrix(2,2,2,1,5,3))(matrix(2,2,9,7,-14,-11)) = (matrix(2,2,4,3,3,2))}}}

{{{(matrix(2,2,(2)(9)+(1)(-14),(2)(7)+(1)(-11),(5)(9)+(3)(-14),(5)(7)+(3)(-11))) = (matrix(2,2,4,3,3,2))}}}

{{{(matrix(2,2,18-14,14-11,45-42,35-33)) = (matrix(2,2,4,3,3,2))}}}

{{{(matrix(2,2,4,3,3,2)) = (matrix(2,2,4,3,3,2))}}}

Edwin</pre>