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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A. If $A$ and $B$ are two invertible matrices, then $(AB)^{-1}=A^{-1}B^{-1}$
B. Every skew symmetric matrix of odd order is invertible
C. If $A$ is non-singular matrix, then $(A^T)^{-1}=(A^{-1})^T$
D. If $A$ is an involutory matrix, then $(I+A)(I-A)=0$
E. A diagonal matrix is both an upper triangular and a lower triangular
Choose the correct answer from the options given below:
Solution
A is false because $(AB)^{-1}=B^{-1}A^{-1}$
B is false since skew symmetric matrix of odd order has determinant zero
C is true
D is true because $A^2=I \Rightarrow (I+A)(I-A)=I-A^2=0$
E is true
Correct statements: C, D, E
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