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Question
If A = `[(1,2),(3,4)]` and X is a 2 × 2 matrix such that AX = I, find X.
Solution
We will reduce the matrix A to the identity matrix by using row transformations. During this process, I will be converted to matrix X.
We have AX = I
∴ `[(1,2),(3,4)] "X" = [(1,0),(0,1)]`
By R2 - 3R1, we get,
`[(1,2),(0,-2)] "X" = [(1,0),(-3,1)]`
By `(-1/2)`R2, we get,
`[(1,2),(0,1)] "X" = [(1,0),(3/2,-1/2)]`
By R1 - 2R2, we get,
`[(1,0),(0,1)] "X" = [(-2,1),(3/2,-1/2)]`
∴ X = `[(-2,1),(3/2,-1/2)]`
Notes
The answer in the textbook is incorrect.
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