Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Determinants

Question:

Which of the following is not true for a square matrix \(A\) of order \(A\)

Options:

The inverse of matrix \(A\), if it exists is unique

If \(A\) is invertible then \(\left(A^{-1}\right)^{-1}=A\)

If \(A\) is invertible then \(\left(A^{T}\right)^{-1}=\left(A^{-1}\right)^{T}\)

If \(A\) is invertible then \(det\left(A\right)=0\)

Correct Answer:

If \(A\) is invertible then \(det\left(A\right)=0\)

Explanation:

If A is invertible, then A must be non-singular. ($A^{-1}$ exist)

$⇒|A|≠0$