### Video Transcript

If the matrix π΄ is equal to five,
five, zero, which of the following is true? Is it (A) the matrix π΄ is a unit
matrix? (B) The matrix π΄ is a diagonal
matrix. (C) The matrix π΄ is a square
matrix. (D) The matrix π΄ is a column
matrix. Or (E) the matrix π΄ is a row
matrix.

We recall that a matrix of order π
by π has π rows and π columns. And if π is equal to π β in other
words, the number of rows is equal to the number of columns β then the matrix is
said to be square. So (C) is the square matrix. But we also know that both unit
matrices and diagonal matrices must themselves be square. And so, letβs ask ourselves, is the
matrix π΄ a square matrix? Well, itβs quite clear that it does
not have the same number of rows and columns. In fact, itβs a one-by-three
matrix. It has one row and three
columns. And so since unit matrices and
diagonal matrices are examples of square matrices, weβre able to disregard the first
three options here. It cannot be any of these.

And so weβre left with two to
choose from. We have column matrix and row
matrix. Well, we know that a column matrix
is such that π is equal to one, we have one column, whereas a row matrix occurs
when π is equal to one, when thereβs one row. Comparing the general form to the
order of our matrix, and we can actually say that π is equal to one and π is equal
to three. We have one row and three columns,
so it cannot be a column matrix. But because π is equal to one, it
must be a row matrix.