Let , where is a real…

MATHEMATICS · Multi-part · CBSE · Mathematics · Determinants · Determinants

Problem

Let

A=\begin{pmatrix}2 & k\\ 3 & 4\end{pmatrix}

, where

k

is a real parameter. (i) Determine the value(s) of

k

for which the matrix

A

is invertible. (ii) For

k = 1

, calculate

A^{-1}

. (iii) Verify your result in part (ii) by showing that

AA^{-1}=I_2

. \newline (Write all intermediate steps clearly.)