If ad - bc ≠ 0, the 2x2 matrix [[a,b],[c,d]] is invertible."

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Multiple Choice

If ad - bc ≠ 0, the 2x2 matrix [[a,b],[c,d]] is invertible."

Explanation:
The key idea is that a square matrix is invertible exactly when its determinant is nonzero. For a 2×2 matrix, the determinant is ad − bc. If ad − bc ≠ 0, the columns are linearly independent, so the matrix has full rank and an inverse exists. In fact, you can write the inverse explicitly as (1/(ad − bc)) times the matrix [[d, −b], [−c, a]]. Therefore, the statement is true.

The key idea is that a square matrix is invertible exactly when its determinant is nonzero. For a 2×2 matrix, the determinant is ad − bc. If ad − bc ≠ 0, the columns are linearly independent, so the matrix has full rank and an inverse exists. In fact, you can write the inverse explicitly as (1/(ad − bc)) times the matrix [[d, −b], [−c, a]]. Therefore, the statement is true.

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