If A = (\begin{bmatrix} 0 & 1 \\\ 0 & 0 \\\ \end{bmatrix}) t... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

If A = $\begin{bmatrix} 0 & 1 \\\ 0 & 0 \\\ \end{bmatrix}$ then $(aI + bA)^n$ is (where I is the identity matrix of order 2)

A

$a^2I + a^{n-1}b \cdot A$

B

$a^n I + na^n b \cdot A$

C

$a^nI + n \cdot a^{n-1} b \cdot A$

D

$a^nI + b^nA$

Answer

$a^nI + n \cdot a^{n-1} b \cdot A$

Explanation

Solution

The correct answer is (C) : anI + n.an-1 b.A.