If A and B are symmetric matrices of the same order, then

**A. ** AB – BA is a symmetric matrix

**B. ** A – B is a skew-symmetric matrix

**C. ** AB + BA is a symmetric matrix

**D. ** AB is symmetric matrix

**Answer : ****Option C**

**Explaination / Solution: **

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.

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If then A is

**A. ** a nilpotent matrix

**B. ** an invertible matrix

**C. ** an idempotent matrix

**D. ** none of these

**Answer : ****Option A**

**Explaination / Solution: **

A square matrix A for which, where n is a positive integer, is called a Nilpotent matrix.

The determinant and trace of the matrix is always Zero for a Nilpotent Matrix.

For the given matrix "A", determinant (A)=0 and trace(A)=0.

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A square matrix A is called idempotent if

**A. ** A2=O
**B. ** 2A=I

**C. ** A2=A
**D. ** A2=I
**Answer : ****Option C**

**Explaination / Solution: **

If the product of any square matrix with itself is the matrix itself , then the matrix is called Idempotent.

If the product of any square matrix with itself is the matrix itself , then the matrix is called Idempotent.

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Let A be any matrix, then can be found only when

**A. ** none of these.

**B. ** m = n

**C. ** m > n

**D. ** m < n

**Answer : ****Option B**

**Explaination / Solution: **

The product of any matrix with itself can be found only when it is a square matrix.i.e. m=n.

The product of any matrix with itself can be found only when it is a square matrix.i.e. m=n.

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If where then A is equal to

**A. **

**B. **

**C. **
**D. **

**Answer : ****Option A**

**Explaination / Solution: **

If where then

If where then

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f A and B are two matrices such that A + B and AB are both defined, then

**A. ** A and B can be any matrices

**B. ** A, B are square matrices not necessarily of same order

**C. ** number of columns of A = number of ros of B.

**D. ** A, B are square matrices of same order

**Answer : ****Option D**

**Explaination / Solution: **

If A and B are square matrices of same order , both operations A + B and AB are well defined.

If A and B are square matrices of same order , both operations A + B and AB are well defined.

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Each diagonal element of a skew-symmetric matrix is

**A. ** Zero

**B. ** negative.

**C. ** Positive

**D. ** non-real

**Answer : ****Option A**

**Explaination / Solution: **

The diagonal elements of a skew-symmetric is zero.

The diagonal elements of a skew-symmetric is zero.

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