# Question Video: Evaluating the Determinant of the Transpose of a Matrix Mathematics

If π΄ is a matrix of order 3 Γ 3 such that det (π΄) = 2, find det (π΄^π).

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### Video Transcript

If π΄ is a matrix of order three by three such that the determinant of π΄ is equal to two, find the determinant of the transpose of π΄.

In this question, weβre given a three-by-three matrix π΄, and weβre told the determinant of this three-by-three matrix is two. We need to use this information to find the value of the determinant of π΄ transpose. The first thing worth noting is the transpose of a matrix replaces its rows with its columns. So since weβre told that π΄ is a three-by-three matrix, the transpose of π΄ is also a three-by-three matrix. This means itβs a square matrix, so we can evaluate its determinant.

In particular, we can evaluate this determinant by recalling if π΄ is any square matrix, then the determinant of π΄ is equal to the determinant of π΄ transpose. Therefore, the determinant of the transpose of π΄ is equal to the determinant of π΄. And weβre told in the question this is equal to two, which means weβve shown if π΄ is a matrix of order three by three such that the determinant of π΄ is equal to two, then the determinant of the transpose of π΄ is also equal to two.