Question

A and B are two matrices ,such that AB = A and BA = B. then what is the value of B square ?

Answer 1

do they both have to be the identity matrix ?

Answer 2

i can't say so.
i think maybe it is.

Answer 3

\[\textbf{AB} = \textbf A\]dividing on the left by \(\textbf{A}\)\[\textbf{B}=\textbf{I}\]

and
\[\textbf{BA} = \textbf{B}\]dividing on the left by \(\textbf B\)\[\textbf A=\textbf I\]

Answer 4

\[\textbf B^2=\]

Answer 5

we need to find the value of \[{B}2\]

Answer 6

Well i just proved \[\textbf B=\textbf I\]

\[\textbf B^2=\textbf I^2=\]

Answer 7

am i making sense ?

Answer 8

how is that possible.can you please elaborate ? @UnkleRhaukus

Answer 9

\[\textbf {II}=\textbf I\]

Answer 10

where is the confusion

Answer 11

thanks @UnkleRhaukus