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swati007
if a diagonal matrix is commutative with every matrix of the same order,then it is necessarily a ______ matrix a. zero matrix b. unit matrix c. scalar matrix d. a symmetric matrix the ans is c... please explain how?... @Mathematics
Consider a general diagonal matrix to be A=[a 0,0,b] and other matrix B=[w x , y z] then compute AB then BA and then equate both which will you a=b which is a scalar matrix ....
Multiplication with an identity matrix is commutative. As every scalar matrix can be written as a product of a scalar and the Identity matrix, most appropriate answer is (c) part. PS: The property will be satisfied by option (a) and (b) also. Every diagonal matrix is a symmetric matrix.