Question

If A is a non-singular matrix, then det(A^–1) = ______.

Options

• 1

• 0

• det(A)

• `1/(det(A)`

Answer 1

If A is a non-singular matrix, then det(A^–1) = `bbunderline(1/(det(A))`.

Explanation:

If A is a non-singular (invertible) matrix, then the determinant of its inverse A⁻¹ is the reciprocal of the determinant of A.

Mathematically, this is expressed as

det(A^–1) = `1/(det(A)`