Singular and Non Singular Matrices

Q.

$IfmatrixA=[a_{ij}{]}_{3\times 3},matrixB=[b_{ij}{]}_{3\times 3}where{a}_{ij}+a_{ji}=0and{b}_{ij}-b_{ji}=0,then|A^4.B^3|is$

1. skew-symmetric matrix

2. singular

3. symmetric

4. zero matrix

Q. Let P and Q be $3\times 3$ matrices such that $P\ne Q.$ If $P^3=Q^{3}and{P}^{2}Q=Q^{2}P,$ then determinant of $(P^2+Q^2)$ is equal to:

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

Q.

What matrix is invertible?

Q. State whether the statement is True or False.

1. True
2. False

Q.

Which among the following are singular matrix /matrices?

1. 

2. 

3. 

4.