Identity Matrix

Q.

Define upper triangular matrix and lower triangular matrix.

Q. An identity matrix is a diagonal matrix in which all of the diagonal elements are equal to .

1. \N
2. 1
3. 2

Q.

If A and B are any two 2×2 matrices such that AB =BA=B IS NOT A zero matrix , what can you say about the matrix A?

Q. If 4^{18}=687194a6735, then the value of a is i)6 ii)3 iii)7 iv)5

Q.

An identity matrix is of the order 2 $\times$ 3. State whether true or false.

1. True

2. False

Q.

IF A and B ar eany two $2\times 2$ matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

Q.

Which among the following can be called as identity matrix/matrices.

1. 

2. 

3. 

4. 

Q.

$\begin{array}{c}AdjointofthematrixN\left[\begin{array}{ccc}-4& -3& -3\\ 1& 0& 1\\ 4& 4& 3\end{array}\right]\end{array}$ is

1. 2N

2. N

3. -N

4. None of these

Q. If A is a $3\times 3$ non-singular matrix such that $A{A}^{\prime }=A^{\prime }A$ and $B=A^{-1}{A}^{\prime }$ then BB' equals

1. $B^{-1}$
2. $\left(B^{-1}\right)$
3. I
4. I + B

Q.

Given $l=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$ Find $l^2$

1. $\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)$

2. $\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$

3. $\left(\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right)$

4. $\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 1& 1& 1\end{array}\right)$

Q. Let $z=\frac{-1+\sqrt{3}i}{2}$, where $i=\sqrt{-1}$, and r, s $ϵ$ {1, 2, 3}. Let $P=\left[\begin{array}{cc}(-z{)}^r& z^{2s}\\ z^{2s}& z^r\end{array}\right]$ and I be the identity matrix of order 2. Then, the total number of ordered pairs (r, s) for which $P^2$ = -I is ___

Q.

Let $A=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$. The only correct statement about the matrix A is

1. A is a zero matrix

2. $A^2=I$

3. A = (-1)I, where I is a unit matrix.

4. $A^{-1}$ does not exist.

Q. Let A, B, C, D be real matrices such that $A^T=BCD;B^T=CDA;C^T=DAB$ and $D^T=ABC$ for the matrix $M=ABCD$, then find $M^{2016}$?

1. $M^2$
2. $M$
3. $M^4$
4. $M^3$

Q.

If a=2^p*3^q*5^r and b=p^2*q^3*r^5 , where p, q, r are primes, find the value of p+q+r, given that a=b.

Q. What is the common difference of an A.P., in which $a_{21}-a_7=644$.

Q. If a $M$ matrix $A$ is such that $A{A}^T=I=A^{T}A$, find $|A|=$?

Q.

Identify the identity matrix from the given list

1. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

2. $\left[\begin{array}{ccc}3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right]$

3. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right]$

4. $\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

Q. An identity matrix is a diagonal matrix in which all of the diagonal elements are equal to .

1. 2
2. 0
3. 1

Q. Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 4& 1& 0\\ 16& 4& 1\end{array}\right]$ and I be the identity matrix of order 3. If $Q=\left[q_{ij}\right]$ is a matrix, such that $P^{50}-Q=I$, then $\frac{q_{31}+q_{32}}{q_{21}}$ equals

1. 52
2. 103
3. 205
4. 201

Q. Let $z=\frac{-1+\sqrt{3}i}{2}$, where $i=\sqrt{-1}$, and r, s $ϵ$ {1, 2, 3}. Let $P=\left[\begin{array}{cc}(-z{)}^r& z^{2s}\\ z^{2s}& z^r\end{array}\right]$ and I be the identity matrix of order 2. Then, the total number of ordered pairs (r, s) for which $P^2$ = -I is ___