List of top Mathematics Questions on Types of Matrices

If a square matrix \( A \) satisfies the condition \( A^T = -A \), then the matrix \( A \) is classified as a:

If \[ A = \begin{bmatrix} 0 & 0 & -5 \\ 0 & 3 & 0 \\ 4.3 & 0 & 0 \end{bmatrix}, \text{ then A is a:} \]

If \( A \), \( B \), and \( C \) are three singular matrices given by \[ A = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 3b & 5 \\ a & 2 \end{bmatrix}, \quad \text{and} \quad C = \begin{bmatrix} a + b + c & c + 1 \\ a + c & c \end{bmatrix}, \] then the value of \( abc \) is:

\(\text{The matrix }\) \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \text{ is a:}\)
(A) Scalar matrix
(B) Diagonal matrix
(C) Skew-symmetric matrix
(D) Symmetric matrix

The Matrix \(M = \begin{bmatrix}        0 & 1 & -1           \\[0.3em]        -1  & 0           &1 \\[0.3em]       1          & -1 & 0     \end{bmatrix}\)is
(A) Symmetric matrix 
(B) Square matrix 
(C) Diagonal matrix
(D) Skew-symmetric matrix
(E) Scalar matrix
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A. \(\begin{bmatrix}1& 2& 3   \\[0.3em]2 & 4 & 5   \\[0.3em]3 & 5&6   \\[0.3em] \end{bmatrix}\) is a Symmetric matrix. 
B. \(\begin{bmatrix}0 &0 &0   \\[0.3em]0& 0&0   \\[0.3em] \end{bmatrix}\) is a Null matrix.
C. \(\begin{bmatrix}1& 0& 0   \\[0.3em]0 & 2 & 0\\[0.3em]0 & 0&3\\[0.3em] \end{bmatrix}\) is an Identity matrix.
D. \(\begin{bmatrix}0& 1&2   \\[0.3em]-1 & 0 & 3   \\[0.3em]-2 & 3&0\\[0.3em] \end{bmatrix}\) is a Skew symmetric matrix.
E. \(\begin{bmatrix}\sqrt{3} &0& 0\\[0.3em]0 & \sqrt{3} & 0   \\[0.3em]0 & 0&\sqrt{3}   \\[0.3em] \end{bmatrix}\) is a Scalar matrix
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Match List - I with List - II.

List - I	List -II
(A) Null Matrix	(I)\(P(A)+P(B)\)
(B) Scaler Matrix	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) Skew-symmetric matrix	(III)\(P(B)-P(A\cap B)\)
(D)Symmetric Matrix	(IV)\(P(B)-P(A\cap B)\)

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The value of λ for which the matrix \(\begin{pmatrix} 1 & 0 & λ \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}\) is a singular matrix is :

Match List-I and List-II

LIST I		LIST II
A.	Singular Matrix	I.	Determinant is always one.
B.	Real Symmetric Matrix	II.	Digonal element are necessarily either purely imaginary or zero
C.	Skew-Hermitian Matrix	III.	Eigen values are always Real
D.	Orthogonal Matrix	IV.	Determinant is always zero

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Match List I with List II

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