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Question
Given A = `[(1 , 1),(8 , 3)]` evaluate A2 - 4A.
Solution
A = `[(1 , 1),(8 , 3)]`
A2 = A x A = `[(1, 1),(8 , 3)][(1 , 1),(8 , 3)]`
= `[(1 + 8 , 1 + 3),(8 + 24, 8 + 9)] = [(9 , 4),(32 , 17)]`
4A = `4[(1 , 1),(8 , 3)] = [(4 , 4),(32 , 12)]`
A2 - 4A = `[(9 , 4),(32 , 17)] - [(4 , 4),(32 , 12)]`
= `[(9 - 4, 4 - 4),(32 - 32, 17 - 12)]`
A2 - 4A = `[(5 , 0),(0 , 5)]`.
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