### Video Transcript

If π΄ is the matrix negative five,
three, negative seven, negative three and π΅ is the matrix negative five, negative
three, negative seven, three, is it true that the matrix π΄ is equal to the matrix
π΅?

We recall for two matrices to be
equal, they need to have the same number of rows and columns and all of their
entries must be identical. We can see that our matrix π΄ has
two rows and two columns and the matrix π΅ also has two rows and two columns. This means to check whether π΄ is
equal to π΅, all we need to do is check whether their entries are identical. Another way of saying this is weβve
shown that the matrix π΄ and the matrix π΅ have the same order. So to check that these two matrices
are equal, we now need to check that all of their entries are identical. Remember, we only compare entries
in the same position in each matrix. And if any of these are not equal,
then we know that our matrices are not equal.

Letβs start with the entry in row
one and column one for both of our matrices. We see the entry in row one and
column one of matrix π΄ is negative five and the entry in row one and column one of
matrix π΅ is also negative five. So these entries are identical. Remember, we need to check this for
all of our entries. Letβs now move on to row two and
column one. This time, we see the entry in row
two and column one of matrix π΄ is negative seven and the entry in row two and
column one of matrix π΅ is also negative seven. So again, these are both equal.

But what happens when we move on to
row one and column two for both of our matrices? In matrix π΄, this value is equal
to three. However, in matrix π΅, this value
is equal to negative three. So the entries in row one and
column two are not equal. And remember for two matrices to be
equal, we must have all of their entries are identical. Therefore, given π΄ is equal to
negative five, three, negative seven, negative three and π΅ is equal to negative
five, negative three, negative seven, three because they have differing entries in
row one column two, we were able to conclude the matrix π΄ is not equal to matrix
π΅.