Consider the $33$ matrix

$724[$A$]=345$

$132$

$($a$)$ Find the inverse $[$A$]1$ and verify that indeed $[$A$]1[$A$]=[$I$],$ where the identity

matrix

$100[$I$]=010$

$001$

$($b$)$Solve the linear system of equations $[$A$][$x$1$ x$2$ x$3]$t $=[91412]$t$,$ using the method of Gaussian elimination via backward substitution. $($Here the super$-$ script t implies transpose which indicates interchange of row and columns. The $[$x$1$ x$2$ x$3]$ is a row matrix; its transpose is a column matrix.$)$