Find-matrix-B-if-given-AB-BA-0-0-0-0-where-A-5-3-5-3-and-B-0-0-0-0-

Question Number 214713 by efronzo1 last updated on 17/Dec/24

Find matrix B if given AB = BA = (\begin{matrix} 0 0 \\ 0 0 \end{matrix})

where A = (\begin{matrix} 5 3 \\ 5 3 \end{matrix}) and B \neq (\begin{matrix} 0 0 \\ 0 0 \end{matrix})

Answered by golsendro last updated on 18/Dec/24

\det (A) = 15 - 15 = 0

so one of possible matrix B is adj (A)

B = adj (A) = (\begin{matrix} 3 - 3 \\ - 5 5 \end{matrix})

verification

(\begin{matrix} 5 3 \\ 5 3 \end{matrix}) (\begin{matrix} 3 - 3 \\ - 5 5 \end{matrix}) = (\begin{matrix} 0 0 \\ 0 0 \end{matrix})

Answered by didoumaths last updated on 17/Dec/24

B = (\begin{matrix} 3 & 3 \\ - 5 & - 5 \end{matrix})

Commented by som(math1967) last updated on 18/Dec/24

B A = (\begin{matrix} 3 & 3 \\ - 5 & - 5 \end{matrix}) (\begin{matrix} 5 & 3 \\ 5 & 3 \end{matrix}) = (\begin{matrix} 30 & 18 \\ - 50 & - 30 \end{matrix})

\neq (\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix})