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No, a square matrix A is not invertible if its determinant |A| is equal to 0. A matrix is invertible (also known as non-singular or non-degenerate) if and only if its determinant is non-zero. If the determinant is zero, the matrix is singular and does not have an inverse.

Invertibility requires that the matrix represents a transformation that can be "undone." When the determinant is zero, it means the matrix collapses space (or at least reduces its dimension), making it impossible to reverse the transformation uniquely.

You can explore more about invertible matrices and their properties on websites such as:

• MathWorld: Invertible Matrix
• Wikipedia: Invertible Matrix