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Transpose of a Matrix - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Transpose of a Matrix is considered one the most difficult concept.
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13 Questions around this concept.
Solve by difficulty
Let $\mathrm{A}$ be a square matrix such that $\mathrm{AA}^{\mathrm{T}}=\mathrm{I}$. Then $\frac{1}{2} \mathrm{~A}\left[\left(\mathrm{~A}+\mathrm{A}^{\mathrm{T}}\right)^2+\left(\mathrm{A}-\mathrm{A}^{\mathrm{T}}\right)^2\right]$ is equal to
Concepts Covered - 1
Transpose of a Matrix
Transpose of a matrix
In simple language transpose of a matrix is changing its rows into columns or columns into rows. Let be a matrix, then matrix obtained by changing rows into columns or vice-versa will give transpose of A which is denoted as A’ or AT. Hence
E.g
Properties of the transpose of a matrix:
If A’ and B’ denotes the transpose of the matrices A and B, then :
i) (A’)’=A
ii) (A±B)’=A’ ± B’ (given that A and B are conformable for matrix addition)
iii) (kA)’ = kA’
iv) (AB)’ = B’A’ ( given that A and B are conformable for matrix product AB)
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