Question

Let A be a non-singular matrix of the order 2 × 2 then |A^-1| =
1. |A|
2. \(\rm \frac {1}{|A|}\)
3. 0
4. None of these

Answer 1

Correct Answer - Option 2 : \(\rm \frac {1}{|A|}\)

Concept:

The determinant of the inverse of an invertible matrix is the inverse of the determinant: \(\det \left( {{{\rm{A}}^{ - 1}}} \right) = \frac{1}{{{\rm{detA}}}}\)

Explanation:

Let A is the second-order matrix,

As we know, AA-1 = I

Taking determinants both sides, we get

⇒ det (AA-1) = det I

⇒ det(A-1) × det (A) = 1              [∵ det (AB) = det A × det B]

∴ det(A-1) = \(\rm \frac {1}{det (A)} = \frac {1}{|A|}\)