Let A= pmatrix 1 & 2 3 & 4 pmatrix , B= pmatrix p & q r & s pmatrix

MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices

Problem

Let

A=\begin{pmatrix}1 & 2\\ 3 & 4\end{pmatrix},\qquad B=\begin{pmatrix}p & q\\ r & s\end{pmatrix}.

It is given that

AB=BA=I_2

. (i) Form the equations that arise from

AB=I_2

and solve them to obtain the values of

p,\,q,\,r,

and

s

. (ii) Show by direct multiplication that the values obtained in part (i) satisfy

BA=I_2

. (iii) Hence write the inverse of

A