Question

Which of the below given matrices has the inverse \(\frac{1}{-6}\begin{bmatrix}2&1\\0&-3\end{bmatrix}\)?

(a) \(\begin{bmatrix}3&-1\\0&2\end{bmatrix}\)

(b) \(\begin{bmatrix}-3&-1\\0&2\end{bmatrix}\)

(c) \(\begin{bmatrix}-2&0\\1&3\end{bmatrix}\)

(d) \(\begin{bmatrix}-3&-1\\0&-2\end{bmatrix}\)

This question was addressed to me in an international level competition.

This question is from Determinants in portion Determinants of Mathematics – Class 12

Answer 1

The correct answer is (b) \(\begin{bmatrix}-3&-1\\0&2\end{bmatrix}\)

The explanation is: Consider the matrix \(\begin{bmatrix}-3&-1\\0&2\end{bmatrix}\)

adj A=\(\begin{bmatrix}2&1\\0&-3\end{bmatrix}\)

|A|=-6

∴A^-1=\(\frac{1}{|A|}\) adj A=\(\frac{1}{-6}\begin{bmatrix}2&1\\0&-3\end{bmatrix}\).