Compute the inverse of a square non-singular matrix A such that A × A⁻¹ = I (identity matrix). Matrix must be square and non-singular (determinant ≠ 0). Uses LU decomposition for numerical stability. Used in portfolio optimization, covariance matrix inversion, solving multiple systems with the same coefficient matrix, and coordinate transformations. Note: For solving Ax=b, direct solving is more efficient than computing A⁻¹ and multiplying.
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Square non-singular matrix (n × n)
[[4, 7], [2, 6]]