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Two nxxn square matrices A and B are sai...

Two `nxxn` square matrices A and B are said to be similar if there exists a non - singular matrix C such that `C^(-1)` AC = B .
If A and B are two singular matrices, then-

A

det(A) = det(B)

B

det(A) + det(B) = 0

C

det(AB) = 0

D

none of these

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The correct Answer is:
A
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Knowledge Check

  • Two nxxn square matrices A and B are said to be similar if there exists a non - singular matrix C such that C^(-1) AC = B . If A and B are similar matrices such that det(A) = 1, then -

    A
    det(B) = 1
    B
    det(A) + det(B) = 0
    C
    det(B) = -1
    D
    none of these

  • Two nxxn square matrices A and B are said to be similar if there exists a non - singular matrix C such that C^(-1) AC = B . If A and B are similar matrices such that det(AB) = 0 then-

    A
    det(A)=0 and det(B) = 0'
    B
    det(A) = 0 or det (B) = 0
    C
    A = 0 and B = 0
    D
    A = 0 or B = 0 [0 =null matrix]

  • In the set all 3xx 3 real matric a relation a relation is defined as follows .A matrix A is related to a matric B if and only if there is a non - singular 3xx 3 matrix P such that B=P^(-1) AP. This relation is -

    A
    reflxice, symmetric but not Transitive
    B
    Reflexive ,Transitive but not symmetric
    C
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    D
    an Equivalence relation

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