On the set `M=A(x)={[xxxx]: x in R}of2x2` matrices, find the identity element for the multiplication of matrices as a binary operation. Also, find the inverse of an element of M.

Explanation

Identity element for the multiplication of matrices as a binary operation.



Let the identity element be `alpha` so `A[alpha]` is a matrix.

`A[x] A[alpha]=A[x]`

`[[x, x], [x, x]][[alpha, alpha], [alpha, alpha]]=[[x, x], [x, x]]`

`[[2x alpha, 2x alpha], [2x alpha, 2x alpha]]=[[x, x], [x, x]]`

`2x alpha=x`

`alpha=1/2`
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