For any square matrix write whether AAT is symmetric or skew-symm… - Vidyadip

Question

For any square matrix write whether AA^T is symmetric or skew-symmetric.

✓

Answer

$\big(\text{AA}^\text{T}\big)^\text{T}=\big(\text{A}^\text{T}\big)^\text{T}\times\text{A}^\text{T}$ $\big\{\text{since, (AB)}^\text{T}=\text{B}^\text{T}\text{A}^\text{T}\big\}$
$\therefore\ \big(\text{AA}^\text{T}\big)^\text{T}=\big(\text{AA}^\text{T}\big)\ \dots(\text{i})$ $\big\{\text{since, }(\text{A}^\text{T})^\text{T}=\text{A}\big\}$
We know that, a square matrix A is symmetric if A^T = A
So, from equation (i)
(AA^T) is a symmetric matric.

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 "2 Marks" from Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate $\int\frac{\text{x}^3-\text{x}^2+\text{x}+1}{\text{x}-1}\text{ dx}$

If $\overrightarrow{ a }=2 \hat{ i }+2 \hat{ j }+3 \hat{ k }, \overrightarrow{ b }=-\hat{ i }+2 \hat{ j }+\hat{ k }$ and $\overrightarrow{ c }=3 \hat{ i }+\hat{ j }$ be such that $\vec{a}+\lambda b$ is perpendicular to vector $\vec{c}$, then find the value of $\lambda$.

Find the integral: $\int \sec x ( \sec x + \tan x ) d x.$

If B is a symmetric matrix, write whether the matrix AB A^T is symmetric or skew-symmetric.

Differentiate the function ${\left( {\log x} \right)^{\cos x}}$ w.r.t. x.

What is the value of the determinant $\begin{vmatrix}0&2&0\\2&3&4\\4&5&6\end{vmatrix}?$

If $\text{A}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\-1&0\end{bmatrix},$ find |AB|.

Evaluate the following:
$\cos^{-1}\Big\{\cos\Big(\frac{4\pi}{3}\Big)\Big\}$

If matrix A = [1 2 3], write AA^T.

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ find $\big(\vec{\text{a}}\times\vec{\text{b}}\big).\vec{\text{b}}.$