Question Video: Properties of the Inverse and Transpose of a Matrix | Nagwa Question Video: Properties of the Inverse and Transpose of a Matrix | Nagwa

# Question Video: Properties of the Inverse and Transpose of a Matrix Mathematics • Third Year of Secondary School

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If π΄ is a matrix, which of the following is equal to (π΄^(β1))^T? [A] (π΄^T)^(β1) [B] π΄^(1/T) [C] (π΄^(β1))^(1/T) [D] π΄^(β1) [E] π΄^T

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### Video Transcript

If π΄ is a matrix, which of the following is equal to π΄ 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 π equals two, one, six, seven, π transpose is equal to two, six, one, seven. To answer this question, we recall the property of the matrix inverse. That is, π΄ transposed inverse is equal to π΄ inverse transposed. And this gives us that our answer is the first option. π΄ inverse transposed is equal to π΄ transposed inverse. So what weβre saying is that if we take the matrix π΄, find its inverse, and then transpose it, this is exactly the same result we would get by taking the matrix π΄, transposing it, and then finding the inverse.

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