Question

Which of the following is the adjoint of the matrix A=\(\begin{bmatrix}1&5\\3&4\end{bmatrix}\)?

(a) \(\begin{bmatrix}4&-5\\-3&-1\end{bmatrix}\)

(b) \(\begin{bmatrix}-4&5\\-3&1\end{bmatrix}\)

(c) \(\begin{bmatrix}4&-5\\-3&1\end{bmatrix}\)

(d) \(\begin{bmatrix}4&5\\-3&1\end{bmatrix}\)

I have been asked this question in class test.

This intriguing question comes from Determinants in portion Determinants of Mathematics – Class 12

Answer 1

Correct answer is (c) \(\begin{bmatrix}4&-5\\-3&1\end{bmatrix}\)

The explanation: We have A11=(-1)^1+1 4=4

A12=(-1)^1+2 3=-3

A21=(1)^2+1 5=-5

A22=(-1)^2+2 1=1

∴adj A=\(\begin{bmatrix}A_{11}&A_{21}\\A_{12}&A_{22}\end{bmatrix}\)=\(\begin{bmatrix}4&-5\\-3&1\end{bmatrix}\).