### Video Transcript

If the order of a zero matrix 𝑂 is
two by two, then the number of elements of the matrix equals what. Nine, zero, four, or the empty set
𝜙.

Let’s begin by recalling what we
mean by the order of a matrix. The order of a matrix tells us how
many rows and how many columns that matrix has. In general, we can specify the
order of a matrix as being 𝑚 by 𝑛. And this means that the matrix has
𝑚 rows and 𝑛 columns. We always specify the number of
rows first and then the number of columns. The matrix we’re interested in in
this question has order two by two, which means that it has two rows and two
columns. It will therefore look a little
something like this: two rows and two columns.

Now we’re actually asked to work
out the number of elements in this matrix, so we can easily count them. There are one, two, three, four
elements in a two-by-two matrix. That’s this option here. Now you may also realize that four
is equal to two times two, the number of rows multiplied by the number of
columns. And this is true in general. The number of elements in the
matrix is equal to the number of rows multiplied by the number of columns. Now, in fact, the matrix in this
question is a zero matrix, which means that every element is equal to zero. So the specific matrix we’re
looking at is the two-by-two matrix zero, zero, zero, zero. But this doesn’t affect our
answer. The number of elements in any
matrix of order two by two is four.