Question

If M = `[(2,1),(1,-2)] `; find M², M³ and M⁵.

Answer 1

`M =[(2,1),(1,-2)] `

 

M^{2 =} `[(2,1),(1,-2)] [(2,1),(1,-2)] = [(4 +1,2 -2),(2-2,1+4)] =[(5,0),(0,5)]`

 

M^{2 =}M²M = `[(2,1),(1,-2)] [(5,0),(0,5)]= [(10 +0,0+ 5),(5-0,0-10)] [(10,5),(5,-10)]`

 

M^{5  =} M² M^{3 =}  `[(5,0),(0,5)][(10,5),(5,-10)]= [(50 +0,25+ 0),(0+25,0      -50)][(50,25),(25,-50)] `