PYQs Learn Notes Mocks Board Formulas Matrices & Determinants
Equality of matrices A = B ⟺ a i j = b i j ∀ i , j A = B \iff a_{ij} = b_{ij} \ \forall\, i,j A = B ⟺ a ij = b ij ∀ i , j a i j , b i j a_{ij}, b_{ij} a ij , b ij corresponding entries Two matrices are equal only when they have the same order and every corresponding pair of entries agrees, which turns one matrix equation into several scalar ones.
2023–2025
years it has appeared
Used alongside How often each of these appears in the same solution as this one.
16 questions whose solution uses this Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.
Filter by exam All exams16 NDA8 CBSE8
Filter by past-year or practice All questions16 Past-year7 Practice9
Showing 16 of 16 questions — easiest first, then oldest paper first.
#1 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
If A = [ 0 3 4 5 ] A = \begin{bmatrix} 0 & 3 \\ 4 & 5 \end{bmatrix} A = [ 0 4 3 5 ] and k A = [ 0 4 a 3 b 60 ] kA = \begin{bmatrix} 0 & 4a \\ 3b & 60 \end{bmatrix} k A = [ 0 3 b 4 a 60 ] then value of k, a and b are respectively #2 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
If A = [ α 0 1 1 ] A = \ \begin{bmatrix}
\alpha & 0 \\
1 & 1
\end{bmatrix} A = [ α 1 0 1 ] and B = [ 1 0 2 1 ] B = \ \begin{bmatrix}
1 & 0 \\
2 & 1
\end{bmatrix} B = [ 1 2 0 1 ] such that A 2 = B , A^{2} = B, A 2 = B , then what is the value of α \alpha α ? ** Matrix A A A has x x x rows and x + 5 x + 5 x + 5 columns. Matrix B B B has y y y rows and 11 − y 11 - y 11 − y columns. Both A B AB A B and B A BA B A exist. #3 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
#4 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
CBSE Class 12 · 2023 · 65/4/1 · Q1 Easy Add #5 · CBSE Class 12 → Mathematics → Matrices → Equality of Matrices
If x [ 1 2 ] + y [ 2 5 ] = [ 4 9 ] x\begin{bmatrix} 1 \\ 2 \end{bmatrix} + y\begin{bmatrix} 2 \\ 5 \end{bmatrix} = \begin{bmatrix} 4 \\ 9 \end{bmatrix} x [ 1 2 ] + y [ 2 5 ] = [ 4 9 ] , then : A x = 1 , y = 2 x = 1,\ y = 2 x = 1 , y = 2 B x = 2 , y = 1 x = 2,\ y = 1 x = 2 , y = 1 C x = 1 , y = − 1 x = 1,\ y = -1 x = 1 , y = − 1 D x = 3 , y = 2 x = 3,\ y = 2 x = 3 , y = 2 CBSE Class 12 · 2023 · 65/5/1 · Q4 Easy Add #6 · CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices
If A = [ 1 0 2 1 ] A = \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix} A = [ 1 2 0 1 ] , B = [ x 0 1 1 ] B = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} B = [ x 1 0 1 ] and A = B 2 A = B^2 A = B 2 , then x x x equals CBSE Class 12 · 2024 · 65/1/1 · Q5 Easy Add #7 · CBSE Class 12 → Mathematics → Matrices → Equality of Matrices
If [ x + y 2 5 x y ] = [ 6 2 5 8 ] \begin{bmatrix} x + y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix} [ x + y 5 2 x y ] = [ 6 5 2 8 ] , then the value of ( 24 x + 24 y ) \left( \frac{24}{x} + \frac{24}{y} \right) ( x 24 + y 24 ) is : CBSE Class 12 · 2024 · 65/4/1 · Q5 Easy Add #8 · CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices
Given that [ 1 x ] [ 4 0 − 2 0 ] = 0 [1 \quad x]\begin{bmatrix} 4 & 0 \\ -2 & 0 \end{bmatrix} = 0 [ 1 x ] [ 4 − 2 0 0 ] = 0 , the value of x x x is : CBSE Class 12 · 2025 · 65/1/3 · Q6 Easy Add #9 · CBSE Class 12 → Mathematics → Matrices → Equality of Matrices
If [ x + y 3 y 3 x x + 3 ] = [ 9 4 x + y x + 6 y ] \begin{bmatrix} x + y & 3y \\ 3x & x + 3 \end{bmatrix} = \begin{bmatrix} 9 & 4x + y \\ x + 6 & y \end{bmatrix} [ x + y 3 x 3 y x + 3 ] = [ 9 x + 6 4 x + y y ] , then ( x − y ) = ? (x - y) = ? ( x − y ) = ? NCERT textbook · Ex 3.1 Q9 Moderate Add #10 · CBSE Class 12 → Mathematics → Matrices → Equality of Matrices
Which of the given values of x x x and y y y make the following pair of matrices equal [ 3 x + 7 5 y + 1 2 − 3 x ] \begin{bmatrix} 3x+7 & 5 \\ y+1 & 2-3x \end{bmatrix} [ 3 x + 7 y + 1 5 2 − 3 x ] , [ 0 y − 2 8 4 ] \begin{bmatrix} 0 & y-2 \\ 8 & 4 \end{bmatrix} [ 0 8 y − 2 4 ] A x = − 1 3 , y = 7 x = \dfrac{-1}{3},\ y = 7 x = 3 − 1 , y = 7 B C y = 7 , x = − 2 3 y = 7,\ x = \dfrac{-2}{3} y = 7 , x = 3 − 2 D x = − 1 3 , y = − 2 3 x = \dfrac{-1}{3},\ y = \dfrac{-2}{3} x = 3 − 1 , y = 3 − 2 Practice question Moderate Add #11 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
If e [ e x e y e y e x ] = [ 1 1 1 1 ] e\begin{bmatrix} e^x & e^y \\ e^y & e^x \end{bmatrix} = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} e [ e x e y e y e x ] = [ 1 1 1 1 ] , then the values of x and y are respectively Practice question Moderate Add #12 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
If ( 2 x + y x + y p − q p + q ) = ( 1 1 0 0 ) \begin{pmatrix} 2x + y & x + y \\ p - q & p + q \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix} ( 2 x + y p − q x + y p + q ) = ( 1 0 1 0 ) , then ( x , y , p , q ) (x, y, p, q) ( x , y , p , q ) equals Practice question Moderate Add #13 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
If X and Y are 2 × 2 2 \times 2 2 × 2 matrices such that 2 X + 3 Y = O 2X + 3Y = O 2 X + 3 Y = O and X + 2 Y = I X + 2Y = I X + 2 Y = I , where O and I denote the 2 × 2 2 \times 2 2 × 2 zero matrix and 2 × 2 2 \times 2 2 × 2 identity matrix, then X = X = X = A [ 1 0 0 1 ] \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} [ 1 0 0 1 ] B [ 2 0 0 2 ] \begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix} [ 2 0 0 2 ] C [ − 3 0 0 − 3 ] \begin{bmatrix} -3 & 0 \\ 0 & -3 \end{bmatrix} [ − 3 0 0 − 3 ] D [ 3 0 0 3 ] \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix} [ 3 0 0 3 ] CBSE Class 12 · 2024 · 65/5/3 · Q5 Moderate Add #14 · CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices
If A = [ x 0 1 1 ] \mathrm{A} = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} A = [ x 1 0 1 ] and B = [ 4 0 − 1 1 ] \mathrm{B} = \begin{bmatrix} 4 & 0 \\ -1 & 1 \end{bmatrix} B = [ 4 − 1 0 1 ] , then value of x x x for which A 2 = B \mathrm{A}^2 = \mathrm{B} A 2 = B is : CBSE Class 12 · 2025 · 65/7/1 · Q7 Moderate Add #15 · CBSE Class 12 → Mathematics → Matrices → Equality of Matrices
If [ 2 x − 1 3 x 0 y 2 − 1 ] = [ x + 3 12 0 35 ] \begin{bmatrix} 2x - 1 & 3x \\ 0 & y^2 - 1 \end{bmatrix} = \begin{bmatrix} x + 3 & 12 \\ 0 & 35 \end{bmatrix} [ 2 x − 1 0 3 x y 2 − 1 ] = [ x + 3 0 12 35 ] , then the value of ( x − y ) (x - y) ( x − y ) is : #16 · NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
If 1 , ω , ω 2 1, \omega, \omega^2 1 , ω , ω 2 are cube roots of unity and if [ 1 + ω 2 ω − 2 ω − b ] + [ a − ω 3 ω 2 ] = [ 0 ω ω 1 ] \begin{bmatrix} 1+\omega & 2\omega \\ -2\omega & -b \end{bmatrix} + \begin{bmatrix} a & -\omega \\ 3\omega & 2 \end{bmatrix} = \begin{bmatrix} 0 & \omega \\ \omega & 1 \end{bmatrix} [ 1 + ω − 2 ω 2 ω − b ] + [ a 3 ω − ω 2 ] = [ 0 ω ω 1 ] , then a 2 + b 2 a^2 + b^2 a 2 + b 2 is A B C D ( 1 + ω ) 2 (1 + \omega)^2 ( 1 + ω ) 2 Every identity this chapter tests, with its own question set.
All Matrices & Determinants formulas 