If $A$ and $B$ are invertible matrices of order $3$ then match List-I with List-II | List-I | List-II | | --- | --- | | (A) $\text{adj}(A)$ | (I) $B^{-1} A^{-1}$ | | (B) $(AB)^{-1}$ | (II) $\vert A\vert ^{-1}$ | | (C) $\vert A^{-1}\vert $ | (III) $\vert A\vert ^2$ | | (D) $\vert \text{adj} A\vert $ | (IV) $\vert A\vert A^{-1}$ | Choose the correct answer from the options given below:

If A is a matrix of order $m \times n$ and B is another matrix such that $A'B$ and $BA'$ are both defined, then the order of matrix B is

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is

Match the LIST-I with LIST-II

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The inverse of the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ is:

Let $A = [a_{ij}]$ be a square matrix of order 3 with $|A| = 2$ and let $C = [c_{ij}]$ where $c_{ij} =$ cofactor of $a_{ij}$ in A. Then $|C|$ is equal to:

If A and B are symmetric matrices of same order, then which of the following statements are true?

(A) $AB^T+B^TA$ is a skew-symmetric matrix.

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

(C) $(AB)^T(A^T)^{-1}=B$

(D) $(AB)^{-1}(BA)^T=A$

Choose the correct answer from the options given below: