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Question
If A = `[(1, 0),(0, -1)]`, find A2 and A3.Also state that which of these is equal to A
Solution
A = `[(1, 0),(0, -1)]`
A2 = A x A = `[(1, 0),(0, -1)][(1, 0),(0, -1)]`
= `[(1 + 0, 0 + 0),(0 + 0, 0 + 1)]`
= `[(1, 0),(0, 1)]`
A3 = A2 + A = `[(1, 0),(0, 1)] xx [(1, 0),(0, -1)]`
= `[(1 + 0, 0 + 0),(0 + 0, 0 - 1)]`
= `[(1, 0),(0, -1)]`
From above it is clear that A3 = A.
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