The matrix is .

Rewrite matrix is A =  .

First find the determinant of  A = ad bc.

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Therefore A^-1 exists.

The inverse of A is .

Substitute a = 1, b = 2, c = 2, d = 1 and ad bc = .

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CHECK:-

Find the product of the matrices.if the product is I, then they are inverses.

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The solution is true.

The inverse matrix is .