Let B= bmatrix 1 & 0 2 & 1 bmatrix and A= bmatrix k & 1 0 & 2 bmatrix

MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices

Problem

Let

B=\begin{bmatrix}1 & 0\\2 & 1\end{bmatrix}\quad\text{and}\quad A=\begin{bmatrix}k & 1\\0 & 2\end{bmatrix},

where

k

is a real number. (i) Compute

AB

and

BA

in terms of

k

. (ii) Determine all real values of

k

for which

AB\neq BA

. (iii) For the value(s) of

k

obtained in part (ii), find the matrix

AB-BA