Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES2 Marks
Question
Let A and B be square matrices of the same order. Does $(A + B)^2 = A^2 + 2AB + B^2$​​​​​​​ hold? If not, why?
✓

Answer

$LHS = (A + B)^2$
$= (A + B)(A + B)$
$= A(A + B) + B(A + B)$
$= A^2 + AB + BA + B^2$
We know that a matrix does not have commutative property. So,
$AB ≠ BA$
Thus,
$(A + B)^2 \neq A^2 + 2AB + B^2$​​​​​​​

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from MATRICES→MATRICES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\sin^2\text{x}\text{ dx}$
→
Prove that the function f given by f (x) = log |cos x| is decreasing on $\left(0, \frac{\pi}{2}\right)$ and increasing on $\left(\frac{3 \pi}{2}, 2 \pi\right)$.
→
Write a value of $\int\text{e}^{\text{ax}}\sin\text{bx}\text{ dx}$
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors such that $\vec{\text{a}}\times\vec{\text{b}}$ is also a unit vector, find the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
→
On expanding by first row, the value of the determinant of $3 \times 3$ square matrix $A = [a_{ij}] is a_{11} C_{11} + a_{12} C_{12} + a_{13} C_{13},$ where $[C_{ij}]$ is the cofactor of $a_{ij}$ in $A.$ Write the expression for its value on expanding by second column.
→
Write the value of $\hat{\text{i}}.\big(\hat{\text{j}}\times\hat{\text{k}}\big)+\hat{\text{j}}.\big(\hat{\text{k}}\times\hat{\text{i}}\big)+\hat{\text{k}}.\big(\hat{\text{i}}\times\hat{\text{j}}\big).$
→
Evaluate the definite integral $\int_{0}^{2} \frac{6 x+3}{x^{2}+4} d x$
→
Determine which of the following binary operations are associative and which are commutative:
'*' on N defined by a * b = 1 for all $\text{a, b}\in\text{N}.$
→
Evaluate:
$\int\limits^3_23^\text{x}\text{ dx}$
→
Evaluate the following:
$\cos\Big(\tan^{-1}\frac{24}{7}\Big)$
→