** Using WeBWorK **

I coded a question to that required the students to input a matrix and I used
answer_matrix(4,4,5) . After looking at recent problems, it would be easier for the students to enter the matrix as a matrix, [[1,2,3,4],....[1,2,3,4]]. I'd like to change the problem to accept the matrix input but it appears I need to change my original array to a matrix object. I don't see how to do this. Previously, my answer checking was element by element, e.g.,
foreach $m (1..4) {

foreach $n (1..4) {
$e2[$m][$n] = 0;
if ($m == $n){
$e2[$m][$n] =1;
if ($m == $k3) {$e2[$m][$n] =$b1};
};
ANS(num_cmp($e2[$m][$n]));
}
}

How do I change the following code

DOCUMENT() ;

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"AnswerFormatHelp.pl",
"parserFunction.pl",
"answerHints.pl",
"PGmatrixmacros.pl",
"PGcourse.pl",
);

############

TEXT(beginproblem());

Context('Matrix');

foreach $i (1..4) {

foreach $j (1..4) {
# original forced only non-zero numbers
# I think they are OK
# $a[$i][$j] = non_zero_random(-10,10,1);
# $b[$i][$j] = non_zero_random(-10,10,1);
$a[$i][$j] = random(-10,10,1);
$b[$i][$j] = random(-10,10,1);

}
}

# part (a)
$k1 = random(1,4,1);
do {$k2 = random(1,4,1)} until ($k2 != $k1);

# part (b)
$k3 = random(1,4,1);
$b1 = non_zero_random(-6,6,1);

# part (c)
$k4 = random(1,4,1);
do {$k5 = random(1,4,1)} until ($k5 != $k4);
$b2 = non_zero_random(-6,6,1);

foreach $m (1..4) {

foreach $n (1..4) {
$e2[$m][$n] = 0;
if ($m == $n){
$e2[$m][$n] =1;
if ($m == $k3) {$e2[$m][$n] =$b1};
};
}
}
$re2 = Compute($e2);

$showPartialCorrectAnswers = 1 ;

BEGIN_TEXT
This problem is related to Problems 5.20 in the text.

$PAR
Consider the following matrix:
$BR
\{ mbox( display_matrix([[$a[1][1], $a[1][2], $a[1][3], $a[1][4]],
[$a[2][1], $a[2][2], $a[2][3], $a[2][4]],
[$a[3][1], $a[3][2], $a[3][3], $a[3][4]],
[$a[4][1], $a[4][2], $a[4][3], $a[4][4]]]) ) \}
$PAR
Write the Elementary Row Operation matrix that:

$PAR
(b) Multiplies row $k3 by $b1 $BR \{ ans_box(4,30)\}


END_TEXT



#answer Part(b)
# first generate identity matrix
# multiply row by b1

ANS($re2->cmp());


ENDDOCUMENT() ;