find the first elements of a column matrix
This would be better as "find the nth element of an array." Also, a column matrix doesn't exist. Perhaps you meant column vector, though the variables in your test cases are row vectors.
Sum of diagonal of a square matrix
Getting the absolute index from a matrix
modulus of a number
Determine whether the input is divisible by 3 as well as 5
Find the last digit
find a specific element from an matrix
find the mean of all elements in a matrix
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