JEE Main Matrices — practice questions
61 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Matrices in the app →A matrix has $3$ rows and $4$ columns. Its order is:The identity matrix $I_n$ of order $n$ is:Two matrices $A$ and $B$ can be multiplied to give $AB$ if and only if:For any matrix $A$, the property $(A^T)^T$ equals:The determinant of the $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is:A square matrix $A$ has an inverse $A^{-1}$ if and only if:A matrix with all elements zero is called:For a 3x3 identity matrix I, det(I) equals:Number of rows in matrix A times number of columns in A x B should equal:The transpose of a 2x3 matrix is a:A square matrix A is symmetric if:The element a_23 of a matrix is located at:If A = [[1,2],[3,4]], find det(A):For A = [[2,0],[0,3]] (diagonal matrix), A² equals:If A is a 3×3 matrix with det(A) = 2, then det(2A):The inverse of a 2x2 matrix [[a,b],[c,d]] is (when det ≠ 0):If A·B = I (identity) and A·C = I, then B equals:For an n × n matrix A, A is invertible if and only if:If A = [[1,2],[3,4]] and B = [[5,6],[7,8]], find A + B:If A is 3×4 and B is 4×2, dimensions of AB:If A is 3×3 and det(A) = 5, then det(A⁻¹) equals:If A is a 3×3 matrix and det(A) = 4, then det(adj A):If A is symmetric and B is skew-symmetric (both n × n), then A + B:For 2x2 matrix A with characteristic equation λ² - 5λ + 6 = 0, the eigenvalues are:By the Cayley-Hamilton theorem, every square matrix satisfies its own:For a 3x3 matrix A, A·(adj A) equals:Rank of the zero matrix:For an orthogonal matrix Q, Q·Qᵀ equals:If A is invertible n × n matrix and B is any n × n matrix, then det(A⁻¹BA):Determinant of [[1,2,3],[4,5,6],[7,8,9]]:Trace of a matrix A is the sum of its:Inverse of [[2,0],[0,3]]:For a 2x2 matrix A with det A = 0, the system Ax = 0 has:For a 3x3 matrix A: (A + Aᵀ) is always:If A = [[1,1],[1,1]], the determinant and rank:A matrix with 3 rows and 4 columns has how many elements?If a matrix has 8 elements, the number of possible orders it can have is:A matrix is called a square matrix when:If $A$ is a matrix of order $m\times n$, then its transpose $A'$ has order:A square matrix $A$ is symmetric if:In a skew-symmetric matrix, all the diagonal elements are:Two matrices can be added only if they have:The product $AB$ of two matrices is defined only when:If $A$ is of order $2\times3$ and $B$ is of order $3\times4$, then $AB$ has order:In a diagonal matrix, all the non-diagonal elements are:For any matrix $A$, $(A')'$ equals:In the identity matrix, the diagonal elements are 1 and all other elements are:If $A=[a_{ij}]$ is a $3\times3$ matrix with $a_{ij}=i+j$, then the element $a_{23}$ is:The product of a matrix $A$ of order $2\times 3$ and $B$ of order $3\times 4$ has order:The transpose of $A^T$ is:A square matrix $A$ is symmetric if:A square matrix $A$ has an inverse if and only if:For matrices A (3×2) and B (2×4), the product AB has order:The transpose of the product (AB)^T equals:Matrix multiplication is:The determinant of the 2×2 matrix [[a, b], [c, d]] equals:A matrix A has an INVERSE if and only if:By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:An ORTHOGONAL matrix A satisfies:The CHARACTERISTIC EQUATION used to find eigenvalues of matrix A is: