If-A-3-4-2-2-1-0-1-1-1-and-B-1-2-2-2-5-4-3-7-5-then-show-that-AB-BA-I-3-

Question Number 104486 by Anindita last updated on 21/Jul/20

If A = [\begin{matrix} 3 & - 4 & 2 \\ - 2 & 1 & 0 \\ - 1 & - 1 & 1 \end{matrix}] and

B = [\begin{matrix} 1 & 2 & - 2 \\ 2 & 5 & - 4 \\ 3 & 7 & - 5 \end{matrix}] then

show that AB = BA = I_{3} .

Answered by OlafThorendsen last updated on 21/Jul/20

Just calculate B^{- 1} = \frac{1}{detB} cov {(B)}^{T}

Then B^{- 1} = A

\Rightarrow AB = B^{- 1} B = I_{3} = {BB}^{- 1} = BA