Matrices · Mathematics · NDA

Let $A$ and $B$ be matrices of order $3 \times 3$. If $|A| = \frac{1}{2 \sqrt{2}}$ and $|B| = \frac{1}{729}$, then what is the value of $|2B(adj(3A))|...

Consider the following statements in respect of two non-singular matrices $A$ and $B$ of the same order $n$: 1.$adj(AB) = (adjA)(adjB)$2. $adj(AB) = a...

Consider the following statements in respect of a non-singular matrix $A$ of order $n$:1. $A(\text{adj}A^T) = A(\text{adj}A)^T$2. If $A^2 = A$, then $...

Consider the following statements in respect of a skew-symmetric matrix $A$ of order $3$:1. All diagonal elements are zero.2. The sum of all the diago...

If $A=\left[\begin{array}{ccc}\sin 2 \theta & 2 \sin ^2 \theta-1 & 0 \\ \cos 2 \theta & 2 \sin \theta \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$,...

If $A=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{array}\right]$, then which of the following ...

If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then what is 23A3 - 19A2 ...

Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ? 1. Its diagonal entries are equal b...

Consider the following statements in respect of square matrices A, B, C each of same order n : 1. AB = AC ⇒ B = C if A is non-singular 2. ...

The system of linear equations x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has  

Let AX = B be a system of 3 linear equations with 3-unknowns. Let X1 and X2 be its two distinct solutions. If the combination aX1 ...

If A = $\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos \theta & \sin \theta \\ 0 & \sin \theta & −\cos \theta\end{array}\r...

If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2, then which of the following are correct? 1. (ZY)X is ...

What is P equal to ?

What is Q equal to ?

Consider the following in respect of the matrices: A = [m n], B = [-n -m] & $ C = \begin{bmatrix} m \\ -m\end{bmatrix} $   1. CA = CB...

If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2\cos \theta & \sin \theta & 0 \\ -1 & 1 & 1 \end{bmatrix},$&...

Let A be a non-singular matrix and B = adj A. Which of the following statements is/are correct? 1. AB = BA 2. AB is a scalar matrix 3. AB can be a ...

Consider the following statements in respect of square matrices A and B of same order : 1. If AB is a null matrix, then at least one of A and B is a ...

Let A and B be non-singular matrices of the same order such that AB = A and BA = B. Which of the following statements is/are correct ? 1. A2 = A...

What is (1110011)2 ÷ (10111)2 equal to ?

If x3 + y3 = (100010111)2 and x + y = (11111)2, then what is (x - y)2 + xy equal to ?