Question

If A=\(\begin{bmatrix}5&-8\\2&6\end{bmatrix}\), find A(adj A).

(a) \(\begin{bmatrix}41&0\\0&46\end{bmatrix}\)

(b) \(\begin{bmatrix}46&0\\1&46\end{bmatrix}\)

(c) \(\begin{bmatrix}46&1\\0&46\end{bmatrix}\)

(d) \(\begin{bmatrix}46&0\\0&46\end{bmatrix}\)

I have been asked this question in an international level competition.

Question is from Determinants in chapter Determinants of Mathematics – Class 12

Answer 1

The correct choice is (d) \(\begin{bmatrix}46&0\\0&46\end{bmatrix}\)

The best explanation: Given that, A=\(\begin{bmatrix}5&-8\\2&6\end{bmatrix}\)

∴adj A=\(\begin{bmatrix}6&8\\-2&5\end{bmatrix}\)

A(adj A)=\(\begin{bmatrix}5&-8\\2&6\end{bmatrix}\begin{bmatrix}6&8\\-2&5\end{bmatrix}\)

=\(\begin{bmatrix}5×6+(-8)×(-2)&5×8+5×(-8)\\2×6+6×(-2)&2×8+6×5\end{bmatrix}\)=\(\begin{bmatrix}46&0\\0&46\end{bmatrix}\).