If $\begin{vmatrix} x-2 & -3 \\ 3x & 2x \end{vmatrix} = 3$, then the values of $x$ are:

If P and Q are non-singular square matrices of the same order, then $(PQ^{-1})^{-1}$ equals

Read the following statements carefully:

A. Determinant is a square matrix

B. If A be any given square matrix of order n, then $A(\text{adj}A) = (\text{adj}A)A = |A|I$.

C. If A and B are nonsingular matrices of the same order, then AB and BA are also nonsingular matrices of the same order.

D. If A is a nonsingular matrix, then its inverse does not exist

Which of the above statements are true?

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Which of the following statements is (are) true?

(A) $B^T AB$ is a skew-symmetric matrix if A is a symmetric matrix

(B) $B^T AB$ is a symmetric matrix if A is a symmetric matrix

(C) $B^T AB$ is a symmetric matrix if A is a skew-symmetric matrix

(D) $B^T AB$ is a skew-symmetric matrix if B is a skew-symmetric matrix

(E) $B^T AB$ is a symmetric matrix if B is a symmetric matrix

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If $A = \begin{bmatrix} 0 & x & x \\ 2y & y & -y \\ z & -z & z \end{bmatrix}$ such that $AA^T=2I$ (where I is an identity matrix of order 3), then which of the following are True?

A. $x^2=1, 3y^2=2$

B. $6y^2=4, 2z^2=3$

C. $9z^2=6, x^2=1$

D. $x^2:y^2:z^2 = 3:1:2$

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If matrix $A=\begin{bmatrix}1 & 4 & 5\\3 & 2 & 6\\0 & 1 & 0\end{bmatrix}$, then

Match List-I with List-II

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Match the LIST-I with LIST-II

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