Question Video: Determining Whether Two Matrices Are Equal or Not Mathematics

Video Transcript

If 𝐴 is the matrix negative five, three, negative seven, negative three and 𝐵 is the matrix negative five, negative three, negative seven, three, is it true that the matrix 𝐴 is equal to the matrix 𝐵?

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 𝐴 has two rows and two columns and the matrix 𝐵 also has two rows and two columns. This means to check whether 𝐴 is equal to 𝐵, all we need to do is check whether their entries are identical. Another way of saying this is we’ve shown that the matrix 𝐴 and the matrix 𝐵 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.

Let’s 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 𝐴 is negative five and the entry in row one and column one of matrix 𝐵 is also negative five. So these entries are identical. Remember, we need to check this for all of our entries. Let’s now move on to row two and column one. This time, we see the entry in row two and column one of matrix 𝐴 is negative seven and the entry in row two and column one of matrix 𝐵 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 𝐴, this value is equal to three. However, in matrix 𝐵, 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 𝐴 is equal to negative five, three, negative seven, negative three and 𝐵 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 𝐴 is not equal to matrix 𝐵.