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Question
If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.
Options
`1/5[(1, 3),(2, -1)]`
`1/5[(3, 1),(2, 1)]`
`1/5[(-3, 2),(4, -1)]`
`1/5[(3, -1),(-2, 1)]`
MCQ
Fill in the Blanks
Solution
If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to `1/5[(3, 1),(2, 1)]`.
Explanation:
A = `[(1, -1),(2, 3)]`
AX = I
⇒ A–1AX = A–1I
⇒ X = A–1
|A| = 5
∴ A–1 = `1/5[(3, 1),(-2, 1)]`
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