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 ...