Algebra

Matrices & Determinants

Easy

common

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ , then $A^{26}$ is equal to

$\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$

$\begin{bmatrix} 26 & 26 \\ 0 & 26 \end{bmatrix}$

$\begin{bmatrix} 1 & 26 \\ 0 & 1 \end{bmatrix}$

$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$

✅ Correct Option: 3

Computing $A^2$ gives first row $(1,2)$ and second row $(0,1)$ . By induction $A^n$ has first row $(1,n)$ and second row $(0,1)$ , so $A^{26}$ has first row $(1,26)$ and second row $(0,1)$ .

2023: 15 June Shift 2

The value of the determinant $\begin{vmatrix} a\cos\theta & b\sin\theta & 0 \\ -b\sin\theta & a\cos\theta & 0 \\ 0 & 0 & c \end{vmatrix}$ is :

2026: 31 May Shift 2

If $A = \begin{bmatrix} 2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4 \end{bmatrix}$ , then $A^2$ is equal to :

2025: 22 May Shift 1

If $\begin{bmatrix} 1 & 2 & 1\end{bmatrix}$ $\begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x\end{bmatrix} = 0,$ then value of x is

2022: 10 Aug Shift 1

The linear equation involving $x$ and $y$ are written in matrix form as:

2025: 3 June Shift 1

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:

2026: 22 May Shift 1

If $A=\begin{bmatrix}1 & 1 & 1\\1 & 0 & 3\\1 & -2 & 1\end{bmatrix}$ , then

Match List-I with List-II

List-I	List-II
(A) $\lvert A\rvert$	(I) 48
(B) $\lvert 2A\rvert$	(II) 36
(C) $\left\lvert\operatorname{adj}(A)\right\rvert$	(III) 12
(D) $2\lvert A\rvert$	(IV) 6

Choose the correct answer from the options given below:

If A=[1101]A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}A=[10​11​], then A26A^{26}A26 is equal to

Solution

Related questions:

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ , then $A^{26}$ is equal to