Consider the matrix

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

Consider the matrix

A=\begin{pmatrix}k & 1\\2 & k\end{pmatrix}

. The

(1,2)

element of

A^{-1}

equals

\dfrac{-1}{k^{2}-2}

. For which value(s) of

k

is this statement true? (a)

k=\pm\sqrt{2}

only (b)

k=\pm\sqrt{3}

k

except

k=\pm\sqrt{2}

(d) All real

k