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