To encode a message, break it into groups of three characters $($including spaces$)$ each, adding spaces at the end if needed. Then, replace each character with an integer $(A=1,$dots,$Z=26,$ space $=27).$ Write each group of three numbers as a column matrix and multiply $B,$ shown at right, by each matrix. To decode an encoded message, write it as column matrices. Multiply $B^{-1}$ by each matrix, then translate the results back to text. Complete parts $($a$)$ through $($c$)$ below.

$($a$)$ Encode the message STAY PUT $.$ Begin by finding the matrix product of B and the first group of three characters into three integers.

$\left[\begin{array}{ccc}2& 4& 6\\ -1& -4& -3\\ 0& 1& -1\end{array}\right]\left[\begin{array}{c}19\\ 20\\ 1\end{array}\right]$

The full message is $124,-102,19,254,-181,11,284,-182,-7.$

$($b$)$ Find the inverse of $B.$

$B^{-1}=$

$($Type a matrix, using an integer or decimal for each matrix element. Do not factor out a scalar multiple.