Question

If X = `[(4, 1),(-1, 2)]`,show that 6X – X² = 9I Where I is the unit matrix.

Answer 1

X = `[(4, 1),(-1, 2)]`

x² = x × x = `[(4, 1),(-1, 2)][(4, 1),(-1, 2)]`

= `[(16 - 1, 4 + 2),(-4 -2 , -1 + 4)]`

= `[(15, 6),(-6, 3)]`

L.H.S. 6X – x² = `6[(4, 1),(-1, 2)]  - [(15, 6),(-6, 3)]`

= `[(24, 6),(-6, 12)] - [(15, 6),(-6, 3)]`

= `[(24 - 15, 6 - 6),(-6 - 6, 12 - 3)]`

= `[(9, 0),(0, 9)]`

= `9[(1, 0),(0, 1)]`
= 91
= R.H.S.
Hence proved.