A matrix and a matrix are given by A= pmatrix 1 & 2 k & 4 pmatrix , B= pmatrix b_ 11…

MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices

Problem

2\times2

matrix

A

and a

2\times2

matrix

B

are given by

A=\begin{pmatrix}1 & 2\\ k & 4\end{pmatrix},\quad B=\begin{pmatrix}b_{11} & b_{12}\\ b_{21} & b_{22}\end{pmatrix},

where

k,\,b_{11},\,b_{12},\,b_{21},\,b_{22}\in\mathbb R

. It is known that

AB=I_2

. (i) Write down the equations obtained by comparing the entries of the product

AB

with those of the identity matrix

I_2

. (ii) Show that

k\neq2

. Explain your reasoning. (iii) Using the equations from part (i), express

b_{11}

and

b_{12}

in terms of

k