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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $A=\begin{bmatrix}2 & -3 \\ 3 & 5\end{bmatrix}$, then which of the following statements are correct?
A. A is a square matrix
B. $A^{-1}$ exists
C. A is a symmetric matrix
D. $|A|=19$
E. A is a null matrix
Choose the correct answer from the options given below.
Solution
Given
$A=\begin{bmatrix}2 & -3 \ 3 & 5\end{bmatrix}$
1.Order of matrix = $2\times 2$
So, A is a square matrix → True
2.Determinant:
$|A|=(2)(5)-(-3)(3)$
$=10+9=19$
Since $|A|\neq 0$, therefore $A^{-1}$ exists → True
3.Transpose:
$A^T=\begin{bmatrix}2 & 3 \ -3 & 5\end{bmatrix}$
Since $A^T\neq A$, so A is not symmetric → False
4. $|A|=19$ → True
5. A is clearly not a null matrix → False
Correct statements: A, B, D
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