### Video Transcript

How many elements are there in a
matrix of order nine by seven?

Remember, we arrange scalars, which
we call elements, in a matrix in rows and columns. When we describe a matrix, letβs
call this general matrix π΄, as an π-by-π matrix, it has π rows and π
columns. And this matrix would look a little
something like this. The order of this matrix is π by
π. Now weβre given a matrix of order
nine by seven. And so this must mean that our
matrix has nine rows and seven columns. So how many elements must it
have?

Well, if we have nine rows and each
of those rows has seven columns and thereβs an element in each of these, then we can
find the number of elements by multiplying nine by seven. Nine times seven is equal to
63. And so, in a matrix of order nine
by seven, there must be a total of 63 elements. And of course, it follows that we
can generalize this and say that a matrix π-by-π order must have π times π
elements.