Multiplication of matrices

Q. If $A=\left[\begin{array}{cc}4& 2\\ -1& 1\end{array}\right]$ and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =

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

Q. The product of two diagonal matrices is always a :-

1. scalar matrix.
2. diagonal matrix.
3. row matrix.
4. identity matrix.

Q.

Add the following expressions using column method:

$2a+3b-9,4a-6b,3a+2b,6a-2b$

Q.

Add the following like terms:

$2aband3ab$

Q.

For two square matrices A and B of the same order, $(A+B)(A-B)$ = $A^2–B^2$.

1. True

2. False

Q.

Find the sum.

$(2w-9)+(-4w-5)$

Q.

Find the sum.$(-2.1m-5)+(3m-7)$

Q.

Find the sum.

$(2n-9)-(-2.4n+4)$

Q. Let A and B be square matrices of same order satisfying AB = A and BA = B. Then $A^2{B}^2$ equals, (O being the zero matrix of the same order as B)

1. A
2. B
3. I
4. O

Q. For two matrices A and B of same order, if AB = A and BA = B then $A^2$is equal to?

1. I (identity matrix)
2. A
3. B
4. $\varphi \left(nullmatix\right)$

Q.

Add the following like terms:

$3xand5x$

Q. Let A =$\left(\begin{array}{cc}p& q\\ r& s\end{array}\right]$ and B =$\left(\begin{array}{c}a\\ b\end{array}\right]$$\ne \left(\begin{array}{c}0\\ 0\end{array}\right]$. Such that AB = B and p+s = 2, then find the value of (ps-qr).

1. 5
2. 1
3. 2
4. 3

Q. If $A=\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$ and $A^2=\left[\begin{array}{cc}\alpha & \beta \\ \beta & \alpha \end{array}\right]$, then

1. $\alpha =a^2+b^2,\beta =ab$
2. $\alpha =a^2+b^2,\beta =2ab$
3. $\alpha =a^2+b^2,\beta =a^2-b^2$
4. $\alpha =2ab,\beta =a^2+b^2$

Q.

Simplify the expression.

$(2r-13)-(-6r+4)$

Q.

Simplify the expression.

$(3j+11)+(8j-7)$

Q.

Add the following like terms:

$-5xand-x$

Q.

If $A=\left[\begin{array}{ccc}1& 2& 1\\ 0& 1& -1\\ 3& -1& 1\end{array}\right]$, then

1. $A^3+3A^2+A-9I_3=0$

2. $A^3-3A^2+A+9I_3=0$

3. $A^3+3A^2-A+9I_3=0$

4. $A^3-3A^2-A+9I_3=0$

Q. In a matrix A of order 3, find $\left(\begin{array}{c}3A\end{array}\right|$?

1. $3\left(\begin{array}{c}A\end{array}\right|$
2. $9\left(\begin{array}{c}A\end{array}\right|$
3. $27\left(\begin{array}{c}A\end{array}\right|$
4. $6\left(\begin{array}{c}A\end{array}\right|$

Q.

If
$A=\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 2& 3& 4\end{array}\right]\text{and}B=\left[\begin{array}{cc}-1& -2\\ -1& 0\\ 2& -1\end{array}\right]$,
then what would be third element in the second column of matrix AB?

1. -8

2. -5
3. 7
4. 5

Q.

$If\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]\text{is the square root of second order unit matrix,}Then\alpha ,\beta and\gamma \text{should satisfy the relation}$

1. $1-{\alpha }^2+\beta \gamma =0$

2. $1-{\alpha }^2-\beta \gamma =0$

3. $1+{\alpha }^2+\beta \gamma =0$

4. ${\alpha }^2+\beta \gamma -1=0$

Q. If $A=\frac{1}{3}\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& -2\\ x& 2& y\end{array}\right]$ is an orthogonal matrix then value of x+y is equal to

1. -3
2. 0
3. 1
4. 3