Question

Which of the below condition is incorrect for the inverse of a matrix A?

(a) The matrix A must be a square matrix

(b) A must be singular matrix

(c) A must be a non-singular matrix

(d) adj A≠0

I got this question in unit test.

Question is taken from Determinants in portion Determinants of Mathematics – Class 12

Answer 1

The correct option is (b) A must be singular matrix

Explanation: The matrix should not be a singular matrix. A square matrix is said to be singular |A|=0.

We know that, A^-1=\(\frac{1}{|A|}\) adj A,

Hence, if |A|=0 the inverse of the matrix does not exist.