Yr 11 matrix help advanced math

shows that matrix A=[1 2] satisfies the matrix equation A^2-5A-2i=0
...............................[ 3 4]


transpose the equation r= 2rn/ n+1 to make n the subject

A^2 7 10
...... 15 22

5A = 5 10
.......15 20

2i = 2 0
.......0 2

So 7 10 ....5 10.....2 0
....15 11 - 15 20 - 0 2 = 0

Edit : the transpose : r = 2 rn / n+1 => r ( n+1 ) = 2rn => n+1 = 2n => n=1

or

r ( n+1 ) = 2rn => n = r(n+1)/2r => n/(n+1) =r/2r

or :

man I hated doing these back in the day... I use to plug and chug it into my TI 83 plus. I dont remember how to do it though. You should look it up if you have that calculator.