If $A = \begin{bmatrix} a & 4 & -5 \\ d & b & -6 \\ 5 & e & c \end{bmatrix}$ is a skew symmetric matrix, then value of $a + b + c + d + e$ is equal to

Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$. If $A^{-1}$ does not exist, then $\lambda =$

If matrix $A = \begin{bmatrix} x & 2 & 3 \\ a & y & -5 \\ b & c & 0 \end{bmatrix}$ is a skew-symmetric matrix, then

(A) $x + y + c = 5$

(B) $c = 5$

(C) $a + b + c = 0$

(D) $a + b - c = 10$

Choose the correct answer from the options given below:

Which of the following statement is/are correct?

(A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$

(B) $A = [a_{ij}]_{m \times m}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$

(C) A square matrix $A = [a_{ij}]$ is called a skew symmetric matrix, if $a_{ij} = -a_{ji}$ for all $i, j$

(D) The multiplication of diagonal matrices of same order is commutative

Choose the correct answer from the options given below:

If $A$ is a square matrix of order 3 such that $|A|=3$, then the value of $|adj(adjA)|$ is equal to

The breadth of plot is:

If a matrix $A = \begin{bmatrix} x+3 & 3 \\ 2x+1 & 5 \end{bmatrix}$ is singular , then the value of $x$ will be