WEBVTT

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Here is the problem: [[4, 7], [2, 6]].

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Find the inverse of a 2 times 2 matrix.

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Check that the determinant is non-zero.

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Swap a and d, negate b and c, divide by the determinant.

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Check: A times A to the power minus 1 equals I.

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So the answer is A to the power minus 1 equals [[3 over 5, negative 7 over 10], [-1 over 5, 2 over 5]].

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The determinant is 10, so A is invertible. Every entry of the inverse is exact.

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Multiplying A by the result gives the identity matrix exactly.