If A= [ cc 4 & 8 -2 & -4 ], prove that A^2=0 - Vidyadip

Question

If $A=\left[\begin{array}{cc}4 & 8 \\ -2 & -4\end{array}\right]$, prove that $A^2=0$

✓

Answer

A2 = A.A

$\begin{aligned} & =\left[\begin{array}{cc}4 & 8 \\ -2 & -4\end{array}\right]\left[\begin{array}{cc}4 & 8 \\ -2 & -4\end{array}\right] \\ & =\left[\begin{array}{cc}16-16 & 32-32 \\ -8+8 & -16+16\end{array}\right] \\ & =\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]=0\end{aligned}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following questions in short." from Determinants and Matrices→Determinants and Matrices — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the acute angle between lines having slopes 3 and −2.

Examine the consistency of following equations.
$x+2 y-3=0, \quad 7 x+4 y-11=0,
2 x+3 y+1=0$

Find the coefficient of variation of a sample that has a mean equal to 25 and a standard deviation of 5.

Show that the matrix $\left[\begin{array}{ccc}x+y & y+z & z+x \\ 1 & 1 & 1 \\ z & x & y\end{array}\right]$ is a singular matrix.

If $A=$, find $\left(A^{\top}\right)^{\top}$.

Write each of the following equations in ax + by + c = 0 form :

$\frac{x}{2}+\frac{y}{4}=1$

A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability that both are yellow?

We know that the y co-ordinate of every point on the X-axis is zero and this is true for points on the X-axis only. Therefore the equation of the X-axis is y = 0.

Find the equation of the line : making intercepts 3 and 6 on the co-ordinate axes.

Find the equation of the line: having slope 5 and containing point A(-1, 2).