Video Transcript
If 𝐴 is a matrix, which of the
following is equal to 𝐴 inverse transpose?
Recall that this notation means the
transpose of a matrix. This just means we switch the rows
with the columns. For example, if we have the matrix
𝑋 equals two, one, six, seven, 𝑋 transpose is equal to two, six, one, seven. To answer this question, we recall
the property of the matrix inverse. That is, 𝐴 transposed inverse is
equal to 𝐴 inverse transposed. And this gives us that our answer
is the first option. 𝐴 inverse transposed is equal to
𝐴 transposed inverse. So what we’re saying is that if we
take the matrix 𝐴, find its inverse, and then transpose it, this is exactly the
same result we would get by taking the matrix 𝐴, transposing it, and then finding
the inverse.
