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Properties of Transpose

April 21, 2018

Properties of Transpose

(i) ( A' )' = A , where A is any matrix.

(ii) ( A + B )' = A' + B' , where A and B are matrix of the same order.

(iii) ( kA )' = kA' , where A is any matrix and k is any number.

(iv) ( AB )' = B'A' , where A and B are matrix for which AB is defined.

properties of transpose transpose

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Relation between Normal Matrix and Identity Matrix

Video Lecture We know that any number remains the same when multiplied by 1. e.g. : Similarly, any matrix remains the same when multiplied by the identity matrix. e.g. : ; where , A is a matrix I is a identity matrix Note : Identity matrix is a square matrix whose diagonal element is 1 and remaining element are zero's . e.g. :

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Properties of Transpose

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