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Question
If A = `[(4, 3, 2),(-1, 2, 0)],"B" = [(1, 2),(-1, 0),(1, -2)]` show that matrix AB is non singular.
Solution
AB = `[(4, 3, 2),(-1, 2, 0)][(1, 2),(-1, 0),(1, -2)]`
= `[(4 - 3 + 2, 8 + 0 - 4),(-1 - 2 + 0, -2 + 0 + 0)]`
= `[(3, 4),(-3, -2)]`
∴ |AB| = `|(3, 4),(-3 ,-2)|`
= – 6 + 12
= 6 ≠ 0
∴ AB is a non-singular matrix.
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