(A) To determine the nature of the matrix $M'AM$,we take its transpose:$(M'AM)' = M'A'(M')'$Using the property of transpose $(ABC)' = C'B'A'$,we get:$

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(A) To determine the nature of the matrix $M'AM$,we take its transpose:$(M'AM)' = M'A'(M')'$Using the property of transpose $(ABC)' = C'B'A'$,we get:$(M'AM)' = M'A'M$Since $A$ is a symmetric matrix,we have $A' = A$.Substituting this into the equation,we get:$(M'AM)' = M'AM$Since the transpose of the matrix $M'AM$ is equal to the matrix itself,$M'AM$ is a symmetric matrix.

Class 12 Mathematics 3-4. Matrices and Determinants Special types of matrices, Transpose of matrices and Trace of matrices

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If $A$ is a symmetric matrix,then the matrix $M'AM$ is

A
Symmetric
B
Skew-symmetric
C
Hermitian
D
Skew-Hermitian

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3-4. Matrices and Determinants

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Special types of matrices, Transpose of matrices and Trace of matrices

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If $A$ is a symmetric matrix,then the matrix $M'AM$ is

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