GATE EC 2014 Set 1 — Question 11
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Engineering Mathematics → Linear Algebra → Matrix Algebra
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Question
For matrices of same dimension , and scalar , which one of these properties DOES NOT ALWAYS hold?
Correct answer
(D) MN = NM
Solution
Let's analyze each property:A.
This property states that the transpose of the transpose of a matrix is the matrix itself. This is always true.B.
This property states that the transpose of a scalar multiple of a matrix is the scalar multiple of the transpose of the matrix. This is always true.C.
This property states that the transpose of the sum of two matrices is the sum of their transposes. This is always true.D.
This property states that matrix multiplication is commutative. However, matrix multiplication is generally not commutative. For example, if and :
Since , this property does not always hold.Therefore, the property that does NOT ALWAYS hold is .The final answer is
This property states that the transpose of the transpose of a matrix is the matrix itself. This is always true.B.
This property states that the transpose of a scalar multiple of a matrix is the scalar multiple of the transpose of the matrix. This is always true.C.
This property states that the transpose of the sum of two matrices is the sum of their transposes. This is always true.D.
This property states that matrix multiplication is commutative. However, matrix multiplication is generally not commutative. For example, if and :
Since , this property does not always hold.Therefore, the property that does NOT ALWAYS hold is .The final answer is
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