Matrix and Determinants

1. A matrix A is both symmetric and skew symmetric if A is

• Null matrix

• unit matrix

• row matrix

• none of these

If A and B are invertible matrix then (AB)^-1 =

• A^-1B^-1

• AB

• B^-1A^-1

• none of these

If A is any invertible matrix then A is

• square matrix

• non singular matrix

• both

• none of these

1. Let A be a square matrix of order 3x3 then| kA| = .

• k |A|

• k²|A|

• k³|A|

• 3k|A|

1. which of the following is correct

• determinants is a square matrix

  
  

• determinants is a number associated to a matrix

• determinants is a number associated to a square matrix

• none of these

If A is an invertible matrix of order 3 and |A|=5 then find |Adj A|

• 5

• 15

• 25

• 125

If A is square matrix of order 3 such that |AdjA| =64 , find |A|

• 64

• 8

• 4

• 192

If the order of matrix A is m×p. And the order of B is p×n. Then the order of matrix AB is

• m × n

• n × m

• n × p

• m × p

When you multiply a matrix by the identity matrix, you obtain the

• inverse matrix.

• transpose matrix.

• Identity matrix

• original matrix.

When you multiply a matrix by the inverse matrix, you obtain the

• inverse matrix.

• transpose matrix.

• Identity matrix

• original matrix.