Scalar Matrix

If A is a square matrix of order n and A=kB, where k is a scalar, then |A|=

1. $|B|$

2. $k^n|B|$

3. $k|B|$

4. $n|B|$

Find x and y if $\left(\begin{array}{cc}2x& 0\\ 0& 3y\end{array}\right)$ is a scalar matrix whose diagonal element is 12

1. x = 6, y = 4

2. x = 12, y = 12

3. x = -6, y = -4

4. x = 4, y = 6

A square matrix $\left(a_{ij}\right)$ where $a_{ij}$= 0 for i $\ne$ j and $a_{ij}$= k (constant) for i = j is called __

1. A triangular matrix
2. A scalar matrix
3. None of these
4. A unit matrix

Which of the following is true about matrix Scalar multiplication kA. Where, A is a matrix & k is a scalar.

1. Both A and B

2. None of these

3. k should be a matrix

4. k should be nonzero

Which of the following is correct about scalar multiplication of a matrix A?

1. Every element of a particular row is multiplied by the scalar when a matrix is multiplied by the scalar.

2. One of the elements of the matrix is multiplied with the scalar when a matrix is multiplied with the scalar.

3. Every element of a particular column is multiplied by the scalar when a matrix is multiplied by the scalar.

4. Every element of the matrix is multiplied with the scalar when a matrix is multiplied with a scalar.

Matrix $A=\left(\begin{array}{ccc}6& 0& 0\\ 0& 6& 0\\ 0& 0& 6\end{array}\right)$ is a ___ matrix

1. Rectangular Matrix

2. Unit Matrix

3. Scalar Matrix

4. Triangular matrix

1. less than 4
2. at least 7 but less than 10
3. at least 4 but less than 7
4. at least 10.

1. True
2. False

If k is scalar $(k\ne 0)$, I is an identity matrix and A is a square matrix . Then which among the following will always be a scalar matrix.

1. kA

2. kI

3. 

4. 

Which among the following is a scalar matrix?