If A be a 3- 3 non-singular matrix and a be a real number then detaA is

If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
(a) null matrix
(b) singular matrix
(c) unit-matrix
(d) non-singular matrix

Q. If

A

is a square matrix of order

3

and

A^{'}

denotes transpose of matrix

A, i f A = A^{'}

and

d e t A = 1

, then

d e t (A - I)

must be equal to

Q. Assertion :If A is skew symmetric matrix of order 3 then its determinant should be zero Reason: If A is square matrix, then

d e t A = d e t A^{'} = d e t (- A^{'})

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If A be a 3×3 non-singular matrix and a be a real number then det(aA) is

The correct option is A a3det(A)Given A is a 3×3 matrix.Now aA gives the matrix obtained by multiplying each element of A by a.Then det(aA)=a3 det(A) [ Since order of A is 3×3]

If $A$ be a $3 \times 3$ non-singular matrix and $a$ be a real number then $d e t (a A)$ is

The correct option is A $a^{3} det (A)$
Given $A$ is a $3 \times 3$ matrix.
Now $a A$ gives the matrix obtained by multiplying each element of $A$ by $a$ .
Then $d e t (a A) = a^{3} d e t (A)$ [ Since order of $A$ is $3 \times 3$ ]