Types of Matrices

Wihch of the following is a diagonal matrix.

Which of the following is a diagonal matrix.

Wihch of the following is a diagonal matrix.

Identify scalar matrix from the following matrices.

The order of the following row matrix $M=\left[\begin{array}{cc}\begin{array}{ccc}\begin{array}{ccc}a& b& c\end{array}& d& e\end{array}& f\end{array}\right]$ is $1\times 5$.

Which of the following represents a column matrix? 

The matrix $\left[\begin{array}{l}a\\ b\\ c\\ d\end{array}\right]$ represents a column matrix.

The matrix $\left[\begin{array}{lll}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$ represents a zero matrix.

If $\left[\begin{array}{cc}a+b& 2\\ 7& ab\\ -3& 4\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 7& 8\\ -3& 4\end{array}\right]$, then

If $\left[\begin{array}{cc}k+4& -1\\ 3& k-6\end{array}\right]=\left[\begin{array}{cc}a& -1\\ 3& -4\end{array}\right]$ then the value of $a$ is

If $\left[\begin{array}{cc}k+4& -1\\ 3& k-6\end{array}\right]=\left[\begin{array}{cc}a& -1\\ 3& -4\end{array}\right]$, then find the value of $a$.

If $\left[\begin{array}{cc}{\tan }^{-1}\frac{1}{2}& \sin x\\ 2{\tan }^{-1}\frac{1}{3}& \tan x\end{array}\right]+\left[\begin{array}{cc}{\tan }^{-1}\frac{1}{3}& 0\\ {\tan }^{-1}\frac{1}{7}& 0\end{array}\right]=\left[\begin{array}{cc}x& \cos x\\ x& \cot x\end{array}\right]$, then find the value of $x$ in degrees.

If $\left[\begin{array}{ccc}{x}^2& 2& 3\\ 4& 7& 2\\ 3& y^2& z^2\end{array}\right]+\left[\begin{array}{ccc}3x& 4& 6\\ 2& -2& t\\ 3& 4y& 8z\end{array}\right]=\left[\begin{array}{ccc}-2& 6& 9\\ 6& 5& 4\\ 6& -3& -12\end{array}\right]$, then find the values of $x, y, z,$ and $t$.

What is the order of the matrix, $\left[\begin{array}{cccc}2& 3& 4& 5\end{array}\right]$?

The element $\text{'}7\text{'}$ is one of the secondary diagonal elements of the square matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$

The element $\text{'}9\text{'}$ is one of the main diagonal elements of the square matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$

A square matrix is such that $A^2=I$, find the value of ${\left(A-I\right)}^3+{\left(A+I\right)}^3-7A$ in simplified form.

For what values of $a$, $b$ and $c$, matrices $A$ and $B$ are equal matrices where

$A=\left[\begin{array}{ccc}a-2& 3& 2c\\ 12c& b+2& bc\end{array}\right]$; $B=\left[\begin{array}{ccc}b& c& 6\\ 6b& a& 3b\end{array}\right]$

If $\left[\begin{array}{cc}2x& 3x+y\\ -x+z& 3y-2p\end{array}\right]=\left[\begin{array}{cc}4& 5\\ -4& -3\end{array}\right]$, then find the values of $x, y, z$ and $p$.

If $\left[\begin{array}{cc}a+b& 2\\ 7& ab\\ -3& 4\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 7& 8\\ -3& 4\end{array}\right]$, then find the values of $a$ and $b$.