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Question
If A = [aij] is a square matrix of order 2 such that aij = `{(1"," "when i" ≠ "j"),(0"," "when" "i" = "j"):},` then A2 is ______.
Options
`[(1,0),(1,0)]`
`|(1,1),(0,0)|`
`|(1,1),(1,0)|`
`[(1,0),(0,1)]`
Solution
If A = [aij] is a square matrix of order 2 such that aij = `{(1"," "when i" ≠ "j"),(0"," "when" "i" = "j"):},` then A2 is `underlinebb([(1,0),(0,1)])`.
Explanation:
aij = `{{:(1",", i ≠ j),(0",", i = j):},`
then A = `[(0, 1),(1, 0)]`
and A2 = `[(0, 1),(1, 0)][(0, 1),(1, 0)] = [(1, 0),(0, 1)]`
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