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Question
Given matrix, X = `[(1, 1),(8, 3)]` and I = `[(1, 0),(0, 1)]`, prove that X2 = 4X + 5I
Solution
X2 = `[(1, 1),(8, 3)][(1, 1),(8, 3)]`
= `[(1 xx 1 + (1) xx (8), 1 xx (1) + (1) xx 3),((8) xx 1 + 3 xx (8),(8) xx (1) + 3 xx 3)]`
= `[(1 + 8, 1 + 3),(8 + 24, 8 + 9)]`
∴ X2 = `[(9, 4),(32, 17)]`
And 4X = `4[(1, 1),(8, 3)]`
= `[(4, 4),(32, 12)]`
4X + 5I = `[(4, 4),(32, 12)] + [(5, 0),(0, 5)]`
= `[(9, 4),(32, 17)]`
∴ X2 = 4X + 5I,
Hence proved
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