query: Prove $(A+B)^2 = A^2 +2AB + B^2$ for commutative matrices
positive_passages.docid: 24809
positive_passages.text: For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
negative_passages.docid: 9986
negative_passages.text: Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
negative_passages.docid: 77064
negative_passages.text: Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
negative_passages.docid: 110703
negative_passages.text: How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
negative_passages.docid: 140252
negative_passages.text: Matrices - Conditions for $AB+BA=0$
negative_passages.docid: 101040
negative_passages.text: Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 123044
negative_passages.text: Commutative matrices are multiples of the identity
negative_passages.docid: 138342
negative_passages.text: Proof of a matrix exponential identity
negative_passages.docid: 85449
negative_passages.text: Show a,b,c congruences when $a^2+b^2=c^2$
negative_passages.docid: 5694
negative_passages.text: How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
negative_passages.docid: 119964
negative_passages.text: Prove: $1/2(a+b) \times (a - b) = b \times a$ - in three space
negative_passages.docid: 115460
negative_passages.text: Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
negative_passages.docid: 11620
negative_passages.text: Is it true that any matrix in $M_2(\mathbb R)$ is the sum of two squares?
negative_passages.docid: 153961
negative_passages.text: Determinant of $2 \times 2$ block matrix with commuting blocks
negative_passages.docid: 123726
negative_passages.text: $2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
negative_passages.docid: 152102
negative_passages.text: Prove that for every complex $2$x$2$ matrix $A$, there exists a matrix $X$ such that $X^3=A^2$.